Drawing ramified coverings with tikz












11















I want to draw a diagram similar to this one:





For that I started with the following code:



begin{tikzpicture}
draw (0,0) node {$Y$};
draw (0,2) node {$X$};
draw[<-] (0,0.35) -- (0,1.65) node[left, midway] {$f$};
draw[thick] (1,0) -- (7,0);
draw[thick] (1,2) -- (7,2);
draw[thick] (1,2.5) -- (7,2.5);
draw[thick] (1,1.5) -- (7,1.5);
end{tikzpicture}


The only thing that I don't know how to do is the curvy parts. I would appreciate some indication.










share|improve this question

























  • Although it doesn't have curvy links, tikz-timing could be useful to draw this kind of diagrams.

    – Ignasi
    19 hours ago
















11















I want to draw a diagram similar to this one:





For that I started with the following code:



begin{tikzpicture}
draw (0,0) node {$Y$};
draw (0,2) node {$X$};
draw[<-] (0,0.35) -- (0,1.65) node[left, midway] {$f$};
draw[thick] (1,0) -- (7,0);
draw[thick] (1,2) -- (7,2);
draw[thick] (1,2.5) -- (7,2.5);
draw[thick] (1,1.5) -- (7,1.5);
end{tikzpicture}


The only thing that I don't know how to do is the curvy parts. I would appreciate some indication.










share|improve this question

























  • Although it doesn't have curvy links, tikz-timing could be useful to draw this kind of diagrams.

    – Ignasi
    19 hours ago














11












11








11


1






I want to draw a diagram similar to this one:





For that I started with the following code:



begin{tikzpicture}
draw (0,0) node {$Y$};
draw (0,2) node {$X$};
draw[<-] (0,0.35) -- (0,1.65) node[left, midway] {$f$};
draw[thick] (1,0) -- (7,0);
draw[thick] (1,2) -- (7,2);
draw[thick] (1,2.5) -- (7,2.5);
draw[thick] (1,1.5) -- (7,1.5);
end{tikzpicture}


The only thing that I don't know how to do is the curvy parts. I would appreciate some indication.










share|improve this question
















I want to draw a diagram similar to this one:





For that I started with the following code:



begin{tikzpicture}
draw (0,0) node {$Y$};
draw (0,2) node {$X$};
draw[<-] (0,0.35) -- (0,1.65) node[left, midway] {$f$};
draw[thick] (1,0) -- (7,0);
draw[thick] (1,2) -- (7,2);
draw[thick] (1,2.5) -- (7,2.5);
draw[thick] (1,1.5) -- (7,1.5);
end{tikzpicture}


The only thing that I don't know how to do is the curvy parts. I would appreciate some indication.







tikz-pgf






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share|improve this question













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share|improve this question








edited 2 days ago









Cragfelt

2,96531028




2,96531028










asked 2 days ago









Gabriel RibeiroGabriel Ribeiro

35519




35519













  • Although it doesn't have curvy links, tikz-timing could be useful to draw this kind of diagrams.

    – Ignasi
    19 hours ago



















  • Although it doesn't have curvy links, tikz-timing could be useful to draw this kind of diagrams.

    – Ignasi
    19 hours ago

















Although it doesn't have curvy links, tikz-timing could be useful to draw this kind of diagrams.

– Ignasi
19 hours ago





Although it doesn't have curvy links, tikz-timing could be useful to draw this kind of diagrams.

– Ignasi
19 hours ago










7 Answers
7






active

oldest

votes


















13














This uses the same in and out trick as Skillmon and puts it into a style dip, which takes as arguments the horizontal position and the depth, where the sign decides whether the dip is a dip (minus) or a bump (plus). (Let me also mention that you do not need to do something like draw[<-] (0,0.35) -- (0,1.65) node[left, midway] {$f$};. If you name the nodes, you can just do draw[<-] (Y) -- (X) node[left, midway] {$f$}; and TikZ will make sure to shorten the arrow without you having to compute the coordinates.)



documentclass[tikz,border=3.14mm]{standalone}
usetikzlibrary{positioning}
newcounter{dip}
begin{document}
begin{tikzpicture}[dip/.style args={#1/#2}{/utils/exec=stepcounter{dip},
insert path={%
coordinate (aux1) ({#1-abs(#2)},0) coordinate (aux2) ({#1+abs(#2)},0) coordinate (aux3)
(aux1) -- (aux2|-aux1) to[out=0,in=180]
++({abs(#2)},#2) coordinate(dip-thevalue{dip}) to[out=0,in=180] (aux3|-aux1)
}}]
begin{scope}[thick,local bounding box=dips]
draw (1,2.5) [dip=5.5cm/-2.5mm]-- (7,2.5);
fill (dip-1) circle[radius=2pt] node[right=3pt]{$b=1$};
draw (1,2) [dip/.list={2.5cm/-2.5mm,5.5cm/2.5mm}] -- (7,2);
fill (dip-2) circle[radius=2pt] node[right=3pt]{$b=1$};
draw (1,1.5) [dip/.list={2.5cm/2.5mm,5.5cm/-5mm}] -- (7,1.5);
fill (dip-5) circle[radius=2pt] node[above right=0pt and 5pt]{$b=2$};
draw (1,1) -- (7,1);
draw (1,0.5) [dip=5.5cm/5mm] -- (7,0.5);
end{scope}
node[left=2pt of dips.west] (X) {$X$};
draw (7,-0.5) -- (1,-0.5) node[left=2pt] (Y) {$Y$};
draw[<-] (Y) -- (X) node[left, midway] {$f$};
foreach X in {1,2}
{
fill (dip-X|-Y) circle[radius=2pt];
draw[dashed] (dip-X|-Y) -- (dip-X|-0,2.75);
}
end{tikzpicture}
end{document}


enter image description here



Just for fun: a variation for Skillmon.



documentclass[tikz,border=3.14mm]{standalone}
usetikzlibrary{positioning}
newcounter{dip}
begin{document}
begin{tikzpicture}[dip/.style={/utils/exec=stepcounter{dip},
insert path={%
to[out=0,in=180]
++(0.25,#1) node[bullet](dip-thevalue{dip}){}
to[out=0,in=180] ++(0.25,-1*#1)
}},bullet/.style={circle,fill,inner sep=1.5pt}]
begin{scope}[thick,local bounding box=dips]
draw (1,2.5) -- (5.25,2.5) [dip=-2.5mm]-- (7,2.5);
node[right=3pt of dip-1]{$b=1$};
draw (1,2) -- (2.25,2) [dip=-2.5mm] -- (5.25,2) [dip=2.5mm] --(7,2);
node[right=3pt of dip-2]{$b=1$};
draw (1,1.5) -- (2.25,1.5) [dip=2.5mm] --(5.25,1.5) [dip=-5mm] -- (7,1.5);
node[above right=-1.5pt and 5pt of dip-5]{$b=2$};
draw (1,1) -- (7,1);
draw (1,0.5) --(5.25,0.5) [dip=5mm] -- (7,0.5);
end{scope}
node[left=2pt of dips.west] (X) {$X$};
draw (7,-0.5) -- (1,-0.5) node[left=2pt] (Y) {$Y$};
draw[<-] (Y) -- (X) node[left, midway] {$f$};
foreach X in {1,2}
{
draw[dashed] (dip-X|-Y) node[bullet]{} -- (dip-X|-0,2.75);
}
end{tikzpicture}
end{document}


enter image description here






share|improve this answer


























  • Very nice automation. Just out of curiosity (coding TikZ is still something I'm not good at), is it possible to also draw the filled circles inside the dip style?

    – Skillmon
    yesterday






  • 1





    @Skillmon Yes, of course. E.g. dip/.style args={#1/#2}{/utils/exec=stepcounter{dip}, insert path={% coordinate (aux1) ({#1-abs(#2)},0) coordinate (aux2) ({#1+abs(#2)},0) coordinate (aux3) (aux1) -- (aux2|-aux1) to[out=0,in=180] ++({abs(#2)},#2) node[circle,fill,inner sep=1.5pt](dip-thevalue{dip}){} to[out=0,in=180] (aux3|-aux1) }}.

    – marmot
    yesterday



















11














The following is a pretty manual way to do this. I only did it for the first two lines, I hope you can apply it to the other occurrences. It uses the in and out keys of the to path construction:



documentclass[tikz]{standalone}

begin{document}
begin{tikzpicture}
draw (0,0) node {$Y$};
draw (0,2) node {$X$};
draw[<-] (0,0.35) -- (0,1.65) node[left, midway] {$f$};
draw[thick] (1,2.5) -- (7,2.5) coordinate(a);
draw[thick] (1,2) -- (7,2) coordinate(b);
draw[thick] (1,1.5) -- (7,1.5) coordinate(c);
draw[thick] (1,0) -- (7,0) coordinate(d);
draw[thick]
(a) ++(.25,-.25) coordinate(ab) to[out=180,in=0] (a)
(ab) to[out=180,in=0] (b)
(ab) to[out=0,in=180] ++(.25,.25)
(ab) to[out=0,in=180] ++(.25,-.25)
;
filldraw
(ab) circle(.05)
;
end{tikzpicture}
end{document}


enter image description here






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    10














    This is a proof of concept how to use parser library to define the following "language" :





    • = stay at the same level


    • u goes half up


    • U goes one up


    • d goes half down


    • D goes one down


    • x plot a (red) dot


    • . end


    Here is the code.



    documentclass[tikz,border=7pt]{standalone}
    usepgfmodule{parser}
    % -----------------------------
    % macro that add #1 to the current path when used inside pgfextra
    definsertpath#1{tikzset{insert path={#1}}}
    % define the parser "sheet path"
    pgfparserdef{sheet path}{initial}{the character =}{insertpath{ -- ++(1, 0)}}
    pgfparserdef{sheet path}{initial}{the letter u}{insertpath{ to[out=0,in=180] ++(1, .5)}}
    pgfparserdef{sheet path}{initial}{the letter U}{insertpath{ to[out=0,in=180] ++(1, 1)}}
    pgfparserdef{sheet path}{initial}{the letter d}{insertpath{ to[out=0,in=180] ++(1,-.5)}}
    pgfparserdef{sheet path}{initial}{the letter D}{insertpath{ to[out=0,in=180] ++(1, -1)}}
    pgfparserdef{sheet path}{initial}{the letter x}{insertpath{ node[red,scale=4]{.}}}
    pgfparserdef{sheet path}{initial}{the character .}{pgfparserswitch{final}}
    % the sheet interface macro
    defsheet#1.{pgfextra{pgfparserparse{sheet path}#1.}}
    % -----------------------------
    begin{document}
    tikzdraw[thick]
    (0,-1) sheet======du=.
    (0,-2) sheet==du==uxd=.
    (0,-3) sheet==uxd==DU=.
    (0,-4) sheet=========.
    (0,-5) sheet======UxD=.;
    end{document}


    enter image description here






    share|improve this answer



















    • 3





      +1, I didn't know parser, wow!

      – CarLaTeX
      yesterday



















    9














    I think Bézier curves can do the task. It can make sure that the starting points and the ending points of all curves are placed with a consistent ratio.



    documentclass[tikz]{standalone}
    definnersep{.5em}
    usetikzlibrary{patterns}
    begin{document}
    begin{tikzpicture}[y=baselineskip+2*innersep]
    draw (0,0)--(6.5,0);
    draw (0,1.5)--(6.5,1.5);
    draw (0,1)--(4.75,1) .. controls (4.9,1) and (4.85,1.5) .. (5,1.5) .. controls (5.15,1.5) and (5.1,1) .. (5.25,1)--(6.5,1);
    draw (0,2)--(1.25,2) .. controls (1.4,2) and (1.35,2.25) .. (1.5,2.25) .. controls (1.65,2.25) and (1.6,2) .. (1.75,2)--(4.75,2) .. controls (4.9,2) and (4.85,1.5) .. (5,1.5) .. controls (5.15,1.5) and (5.1,2) .. (5.25,2)--(6.5,2);
    draw (0,2.5)--(1.25,2.5) .. controls (1.4,2.5) and (1.35,2.25) .. (1.5,2.25) .. controls (1.65,2.25) and (1.6,2.5) .. (1.75,2.5)--(4.75,2.5) .. controls (4.9,2.5) and (4.85,2.75) .. (5,2.75) .. controls (5.15,2.75) and (5.1,2.5) .. (5.25,2.5)--(6.5,2.5);
    draw (0,3)--(4.75,3) .. controls (4.9,3) and (4.85,2.75) .. (5,2.75) .. controls (5.15,2.75) and (5.1,3) .. (5.25,3)--(6.5,3);
    fill (1.5,2.25) circle (1.5pt) (5,1.5) circle (1.5pt) (5,2.75) circle (1.5pt) (1.5,0) circle (1.5pt) (5,0) circle (1.5pt);
    draw[dashed] (1.5,0)--(1.5,3.25) (5,0)--(5,3.25);
    draw (1.5,2.25) node[right=1ex] {$b=1$};
    draw (5,1.75) node[right=1ex] {$b=2$};
    draw (5,2.75) node[right=1ex] {$b=1$};
    draw (-0.5,0) node (n) {$N$};
    draw (-0.5,2.25) node (m) {$M$};
    draw[-latex] (m)--(n) node[midway,left] {$f$};
    end{tikzpicture}
    end{document}


    enter image description here






    share|improve this answer































      6














      This is a proof of concept how to use plot[smooth] coordinates to do this.



      documentclass[tikz,border=7pt]{standalone}
      begin{document}
      begin{tikzpicture}[yscale=.5,
      sheet/.style={red,thick,smooth},
      point/.style={insert path={node[scale=4]{.}}}]
      % ---- sheets ----
      foreach[count=i] pts in {
      {(0, 0) (1, 0) (2, 0) (3, 0) (6, 0) (7,-1) (8, 0) (9, 0)},%
      {(0, 0) (1, 0) (2,-1) (3, 0) (6, 0) (7, 1) (8, 0) (9, 0)},%
      {(0, 0) (1, 0) (2, 1) (3, 0) (6, 0) (7,-2) (8, 0) (9, 0)},%
      {(0, 0) (1, 0) (2, 0) (3, 0) (6, 0) (7, 0) (8, 0) (9, 0)},%
      {(0, 0) (1, 0) (2, 0) (3, 0) (6, 0) (7, 2) (8, 0) (9, 0)},%
      {(0,0)},%
      {(0, 0) (9, 0)}%
      }{
      draw[yshift=-2*i cm,sheet] plot coordinates {pts};
      }
      % ---- singular points and labels ----
      path
      (2,-5) [point] (3,-5) node{$b=1$}
      (7,-3) [point] (8,-3) node{$b=1$}
      (7,-8) [point] (8,-7.5) node{$b=2$}
      ;
      % ---- vertical lines ----
      draw[dashed]
      (2,0) -- +(0,-14) [point]
      (7,0) -- +(0,-14) [point]
      ;
      end{tikzpicture}
      end{document}


      enter image description here






      share|improve this answer































        5














        This is a proof of concept how to use turtle library to define the following "moves" :





        • up make an up bump


        • up* make an up bump with (red) dot


        • dn make a down bump


        • dn* make a down bump with (red) dot


        • * put a (red) dot


        documentclass[tikz,border=7pt]{standalone}
        usetikzlibrary{turtle}
        tikzset{
        turtle/.cd,
        how/.style={out=0,in=180},
        home/.append style=right,
        */.style={/tikz/insert path={node[red,scale=4]{.}}},
        forward/.default=1.4142135,
        up/.style={left=45,forward,right,forward,left=45},
        up*/.style={left=45,forward,*,right,forward,left=45},
        dn/.style={right=45,forward,left,forward,right=45},
        dn*/.style={right=45,forward,*,left,forward,right=45},
        next/.style={/tikz/yshift=-1cm}
        }

        begin{document}
        tikz
        draw[thick]
        [turtle={home,fd,fd,fd,fd,fd,fd,dn,fd},next,next]
        [turtle={home,fd,fd,dn,fd,fd,up*,fd},next,next]
        [turtle={home,fd,fd,up*,fd,fd,dn,fd},next]
        [turtle={home,fd,fd,fd,fd,fd,fd,fd,fd,fd},next]
        [turtle={home,fd,fd,fd,fd,fd,fd,up*,fd}]
        ;
        end{document}


        enter image description here






        share|improve this answer































          5














          Edit notes:




          • spaces can now be handled, but are ignored by default


          • alternative syntax for myparserdef added





          Inspired by Kpym's answer but thinking that the possibilities of pgfparser are insufficient, I wrote my own parser, that should be similar to pgf's, but allows the parsed elements to grab arguments. The following arguments are supported:





          • m a mandatory argument


          • r{<delim>} a mandatory argument delimited by <delim>


          • o an optional argument in brackets (you can test for it with myIfNoValueTF)


          • O{<default>} an optional argument defaulting to <default>


          • d<delim1><delim2> an optional argument delimited by <delim1> and <delim2> (you can test for it with myIfNoValueTF)


          • D<delim1><delim2>{<default>} an optional argument delimited by <delim1> and <delim2> defaulting to <default>


          • t<token> an optional token (you can test for it with myIfBooleanTF)


          Despite the fact that the argument names are inspired by xparse, none of them care for balanced delimiters (e.g., [[ab]] would not be grabbed as [ab], but as [ab with an orphaned ], so you'd have to use [{[ab]}], this is like the LaTeX2e behaviour). Also all arguments are long by nature unlike xparse where you'd need to specify that using +.



          You can define a parser using myparserdef{<name>}{<state>}{<meaning>}[<args>]{<code>}, with <name> the name of the parser, <state> the state, <meaning> the meaning of a token, <args> an argument string (built from the arguments listed above, up to 9 arguments are supported) and <code> the code which should be executed for that combination of <name>, <state> and <meaning>. You can switch states using myparserstate{<state>}, if you switch to final parsing is ended, the initial state is initial. All in all this is pretty similar to pgfparsers way of doing things. The biggest difference is, that my parser ignores blanks by default, however you can define an action for blanks with myparserdef{<name>}{<state>}{blank space}[<args>]{<code>}. Many consecutive blanks are considered as one.



          You can also use a different syntax for myparserdef namely: myparserdef{<name>}{<state>}<token>[<args>]{<code>} with <token> being a single token not surrounded by {} (spaces are ignored here, it is not checked whether <token> is really a single token, so be careful). In that case the same will be done as if you'd typed the meaning of the <token>, so myparserdef{foo}{bar}a{baz} does the same as myparserdef{foo}{bar}{the letter a}{baz}.



          A parser is executed using myparserrun{<name>}. A parser needs at least one rule, else an error is thrown.



          This parser system allows me to place coordinates inside of sheet, which was the main reason why I found pgfparser insufficient.



          I did all of this without using any packages, only LaTeX-Kernel macros, just for procrastinating reasons. Using for example xparse would shorten the code considerably.



          documentclass[tikz,border=7pt]{standalone}

          % my parser >>>
          makeatletter
          % logic helpers >>>
          longdefmyfi@An#1fi#2{fi}
          longdefmyfi@Ay#1fi#2{fi#2}
          longdefmyfi@Byfi#1{fi#1}
          longdefmyfi@BTbfi#1#2#3{fi#2}
          % <<<
          % mynewdef >>>
          @ifdefinablemyifundefTF%>>>
          {%
          defmyifundefTF#1%
          {%
          ifdefined#1%
          myfi@Ay
          else
          myfi@BTb
          fi
          {%
          ifx#1relax
          myfi@BTb
          fi
          @secondoftwo
          }%
          }%
          }%<<<
          @ifdefinablemynewdef%>>>
          {%
          protecteddefmynewdef{@ifnextchar[{mynewdef@a}{mynewdef@a}}%
          }%<<<
          @ifdefinablemynewdef@a%>>>
          {%
          longdefmynewdef@a[#1]#2#3#{mynewdef@b{#1}#2{#3}}%
          }%<<<
          @ifdefinablemynewdef@b%>>>
          {%
          protectedlongdefmynewdef@b#1#2#3#4%
          {%
          myifundefTF#2%
          {%
          #1def#2#3{#4}%
          }
          {%
          PackageError{my}{Command string#2space already defined}{}%
          }
          }%
          }%<<<
          mynewdefmyifcsundefTF#1%>>>
          {%
          ifcsname #1endcsname
          myfi@Ay
          else
          myfi@BTb
          fi
          {%
          expandafterifxcsname #1endcsnamerelax
          myfi@BTb
          fi
          @secondoftwo
          }%
          }%<<<
          % <<<
          % opt arg parsing >>>
          mynewdef[long]my@ifmark#1%>>>
          {%
          ifxmy@mark#1%
          myfi@BTb
          fi
          @secondoftwo
          }%<<<
          mynewdef[protectedlong]myoarg@oarg#1%>>>
          {%
          @ifnextchar[{myoarg@oarg@{#1}}{#1{my@mark}}%
          }%<<<
          mynewdef[long]myoarg@oarg@#1[#2]%>>>
          {%
          #1{#2}%
          }%<<<
          mynewdef[protectedlong]myoarg@Oarg#1#2%>>>
          {%
          @ifnextchar[{myoarg@oarg@{#2}}{#2{#1}}%
          }%<<<
          mynewdef[protectedlong]myoarg@darg#1#2#3%>>>
          {%
          longdefmyoarg@darg@##1#1##2#2{##1{##2}}%
          @ifnextchar#1{myoarg@darg@{#3}}{#3{my@mark}}%
          }%<<<
          mynewdef[protectedlong]myoarg@Darg#1#2#3#4%>>>
          {%
          longdefmyoarg@darg@##1#1##2#2{##1{##2}}%
          @ifnextchar#1{myoarg@darg@{#4}}{#4{#3}}%
          }%<<<
          % <<<
          % macros for string comparison >>>
          begingroupdef:{endgroupletmy@sptoken= }:
          mynewdefmy@mark{my@mark@if@you@see@this@report@it}
          mynewdefmy@stop{my@stop@if@you@see@this@report@it}
          mynewdefmyparser@final{final}
          mynewdefmyparser@noarg{noarg}
          mynewdefmyparser@blankspace{blank space}
          % <<<
          mynewdef[protected]myparserdef#1#2%>>>
          {%
          defmyparserdef@twoargs{{#1}{#2}}%
          myparserdef@a
          }%<<<
          mynewdef[protected]myparserdef@a%>>>
          {%
          futureletmyparserdef@argmyparserdef@b
          }%<<<
          mynewdefmyparserdef@b%>>>
          {%
          ifxmyparserdef@argmy@sptoken
          myfi@BTb
          fi
          @secondoftwo
          {myparserdef@gobble@space}
          {myparserdef@c}%
          }%<<<
          mynewdef[protected]myparserdef@gobble@space%>>>
          {%
          afterassignmentmyparserdef@a
          letmyparserdef@arg= % space after = to get spaces, too
          }%<<<
          mynewdef[protected]myparserdef@c#1%>>>
          {%
          ifxmyparserdef@argbgroup
          myfi@BTb
          fi
          @secondoftwo
          {%
          defmyparserdef@arg{#1}%
          ifxmyparser@blankspacemyparserdef@arg
          myfi@BTb
          fi
          @secondoftwo
          {expandaftermyparserdef@dmyparserdef@twoargs{blank space space}}
          {expandaftermyparserdef@dmyparserdef@twoargs{#1}}%
          }
          {expandaftermyparserdef@dmyparserdef@twoargs{meaningmyparserdef@arg}}%
          }%<<<
          mynewdef[long]myparserdef@d#1#2#3%>>>
          {%
          myoarg@oarg{myparserdef@e{#1}{#2}{#3}}%
          }%<<<
          mynewdef[protectedlong]myparserdef@e#1#2#3#4#5%>>>
          {%
          % if that is the first rule for the parser, define space to be a no-op
          myifcsundefTF{myparser@name{#1}}%
          {%
          expandafterdef
          csname myparser@name{#1} all blank space spacespace typeendcsname
          {noarg}%
          expandafterdef
          csname myparser@name{#1} all blank space spacespace codeendcsname
          {myparser@getnexttoken}%
          % use a macro as a flag that there is at least one parser rule defined
          expandafterdefcsnamemyparser@name{#1}endcsname{}%
          }
          {}%
          % check whether the optional argument was used
          my@ifmark{#4}
          {%
          % use a macro as flag that there is a rule for the specified state
          expandafterdefcsname myparser@name{#1} #2 #3 typeendcsname{noarg}%
          defmyparserdef@arg@count{0}%
          }
          {%
          edefmyparserdef@arg@count
          {thenumexprmyparserdef@argcount#4my@mark}%
          ifnummyparserdef@arg@count>9%
          PackageError{my}{Too many arguments for parser rule}
          {A maximum of 9 parameters is supported.}%
          else
          ifnummyparserdef@arg@count=0%
          expandafterdefcsname myparser@name{#1} #2 #3 typeendcsname
          {noarg}%
          else
          expandafterdefcsname myparser@name{#1} #2 #3 typeendcsname{#4}%
          fi
          fi
          }%
          % define what the code does
          expandafterdefcsname myparser@name{#1} #2 #3 codeendcsname{}%
          expandafterrenewcommandcsname myparser@name{#1} #2 #3 codeendcsname
          [myparserdef@arg@count]{#5myparser@getnexttoken}%
          }%<<<
          mynewdefmyparserdef@argcount#1%>>>
          {%
          ifxmy@mark#1%
          myfi@An
          else
          myfi@By
          fi
          {csname myparserdef@argcount@#1endcsname}%
          }%<<<
          mynewdefmyparserdef@argcount@m%>>>
          {%
          +1%
          myparserdef@argcount
          }%<<<
          mynewdefmyparserdef@argcount@o%>>>
          {%
          +1%
          myparserdef@argcount
          }%<<<
          mynewdefmyparserdef@argcount@O#1%>>>
          {%
          +1%
          myparserdef@argcount
          }%<<<
          mynewdefmyparserdef@argcount@d#1#2%>>>
          {%
          +1%
          myparserdef@argcount
          }%<<<
          mynewdefmyparserdef@argcount@D#1#2#3%>>>
          {%
          +1%
          myparserdef@argcount
          }%<<<
          mynewdefmyparserdef@argcount@r#1%>>>
          {%
          +1%
          myparserdef@argcount
          }%<<<
          mynewdefmyparserdef@argcount@t#1%>>>
          {%
          +1%
          myparserdef@argcount
          }%<<<
          mynewdefmyparser@name#1%>>>
          {%
          myparser #1%
          }%<<<
          mynewdefmyparser@rule#1%>>>
          {%
          myparser@currentspace #1space meaningmyparser@token
          }%<<<
          mynewdefmyparser@type#1%>>>
          {%
          myparser@rule{#1} type%
          }%<<<
          mynewdefmyparser@code#1%>>>
          {%
          myparser@rule{#1} code%
          }%<<<
          mynewdef[protected]myparserrun#1%>>>
          {%
          myifcsundefTF{myparser@name{#1}}
          {PackageError{my}{No parser named '#1' defined}{}}
          {%
          edefmyparser@current{myparser@name{#1}}%
          defmyparser@usersname{#1}%
          defmyparser@state{initial}%
          myparser@getnexttoken
          }%
          }%<<<
          mynewdef[protected]myparser@getnexttoken%>>>
          {%
          ifxmyparser@statemyparser@final
          myfi@An
          else
          myfi@By
          fi
          {%
          afterassignmentmyparser@getnexttoken@a
          letmyparser@token= % space after = to get spaces, too
          }%
          }%<<<
          mynewdef[protected]myparser@getnexttoken@a%>>>
          {%
          myifcsundefTF{myparser@type{myparser@state}}
          {%
          myifcsundefTF{myparser@type{all}}
          {%
          PackageError{my}
          {%
          No rule for parser 'myparser@usersname' in state
          'myparser@state' for 'meaningmyparser@token'.
          Ignoring token%
          }
          {}%
          myparser@getnexttoken
          }
          {myparser@handle{all}}%
          }
          {myparser@handle{myparser@state}}%
          }%<<<
          mynewdef[protected]myparser@handle#1%>>>
          {%
          expandafterifxcsnamemyparser@type{#1}endcsnamemyparser@noarg
          myfi@BTb
          fi
          @secondoftwo
          {csnamemyparser@code{#1}endcsname}
          {myparser@handle@args{#1}}%
          }%<<<
          mynewdef[protected]myparserstate#1%>>>
          {%
          defmyparser@state{#1}%
          }%<<<
          mynewdef[protected]myparser@handle@args#1%>>>
          {%
          defmyparser@stateorall{#1}%
          expandafterexpandafterexpandaftermyparser@handle@args@a
          csnamemyparser@type{#1}endcsnamemy@markmy@stop
          }%<<<
          mynewdefmyparser@handle@args@a%>>>
          {%
          myparser@handle@args@b{}%
          }%<<<
          mynewdef[long]myparser@handle@args@b#1#2#3my@stop%>>>
          {%
          my@ifmark{#2}
          {csnamemyparser@code{myparser@stateorall}endcsname#1}
          {%
          myifcsundefTF{myparser@handle@args@#2}
          {PackageError{my}{Unknown argument type '#2'}{}}
          {csname myparser@handle@args@#2endcsname{#1}{#3}}%
          }%
          }%<<<
          mynewdef[long]myparser@handle@args@c#1#2%>>>
          {%
          my@ifmark{#2}
          {csnamemyparser@code{myparser@stateorall}endcsname#1}
          {myparser@handle@args@b{#1}#2my@stop}%
          }%<<<
          mynewdef[long]myparser@handle@args@m#1#2#3%>>>
          {%
          myparser@handle@args@c{#1{#3}}{#2}%
          }%<<<
          mynewdef[protectedlong]myparser@handle@args@o#1#2%>>>
          {%
          myoarg@oarg{myparser@handle@args@m{#1}{#2}}%
          }%<<<
          mynewdef[long]myparser@handle@args@O#1#2%>>>
          {%
          myparser@handle@args@O@{#1}#2my@stop
          }%<<<
          mynewdef[protectedlong]myparser@handle@args@O@#1#2#3my@stop%>>>
          {%
          myoarg@Oarg{#2}{myparser@handle@args@m{#1}{#3}}%
          }%<<<
          mynewdef[long]myparser@handle@args@d#1#2%>>>
          {%
          myparser@handle@args@d@{#1}#2my@stop
          }%<<<
          mynewdef[protectedlong]myparser@handle@args@d@#1#2#3#4my@stop%>>>
          {%
          myoarg@darg{#2}{#3}{myparser@handle@args@m{#1}{#4}}%
          }%<<<
          mynewdef[long]myparser@handle@args@D#1#2%>>>
          {%
          myparser@handle@args@D@{#1}#2my@stop
          }%<<<
          mynewdef[protectedlong]myparser@handle@args@D@#1#2#3#4#5my@stop%>>>
          {%
          myoarg@Darg{#2}{#3}{#4}{myparser@handle@args@m{#1}{#5}}%
          }%<<<
          mynewdef[long]myparser@handle@args@r#1#2%>>>
          {%
          myparser@handle@args@r@a{#1}#2my@stop
          }%<<<
          mynewdef[protectedlong]myparser@handle@args@r@a#1#2#3my@stop%>>>
          {%
          defmyparser@handle@args@r@b##1#2{myparser@handle@args@c{#1{##1}}{#3}}%
          myparser@handle@args@r@b
          }%<<<
          mynewdef[long]myparser@handle@args@t#1#2%>>>
          {%
          myparser@handle@args@t@a{#1}#2my@stop
          }%<<<
          mynewdef[protectedlong]myparser@handle@args@t@a#1#2#3my@stop%>>>
          {%
          @ifnextchar#2%
          {@firstoftwo{myparser@handle@args@c{#1{my@mark}}{#3}}}
          {myparser@handle@args@c{#1{my@stop}}{#3}}%
          }%<<<
          letmyIfNoValueTFmy@ifmark
          letmyIfBooleanTFmy@ifmark
          makeatother
          % <<<

          % the sheet path parser >>>
          makeatletter
          definsertpath#1{edefsheetpath@{unexpandedexpandafter{sheetpath@#1}}}
          defsheetpathcurve#1#2#3#4%
          {%
          to[out=0,in=180] ++({.5*sheetlength},{#1*sheetheight})
          myIfBooleanTF{#3}{}{node[scale=sheetdotsize,inner sep=0pt]{.}}
          myIfNoValueTF{#4}{}{coordinate({#4})}
          to[out=0,in=180] ++({.5*sheetlength},{#2*sheetheight})
          }
          defoutputpath{drawsheetpath@;}
          defsheet{defsheetpath@{}myparserrun{sheet path}}
          makeatother
          myparserdef{sheet path}{initial}{the character (}[r,r)]
          {insertpath{({#1},{#2*sheetheight})}myparserstate{started}}
          myparserdef{sheet path}{initial}{the character =}
          {insertpath{(0,0)--++(sheetlength,0)}myparserstate{started}}
          myparserdef{sheet path}{started}{the character (}[r)]
          {insertpath{coordinate({#1})}}
          myparserdef{sheet path}{started}{the character =}
          {insertpath{--++(sheetlength,0)}}
          myparserdef{sheet path}{started}{the letter u}[txd()]
          {insertpath{sheetpathcurve{.5}{-.5}{#1}{#2}}}
          myparserdef{sheet path}{started}{the letter U}[txd()]
          {insertpath{sheetpathcurve{1}{-1}{#1}{#2}}}
          myparserdef{sheet path}{started}{the letter d}[txd()]
          {insertpath{sheetpathcurve{-.5}{.5}{#1}{#2}}}
          myparserdef{sheet path}{started}{the letter D}[txd()]
          {insertpath{sheetpathcurve{-1}{1}{#1}{#2}}}
          % making '.' a no-op, that way we can use it to end the search for an optional
          % argument for instance
          myparserdef{sheet path}{started} .{}
          myparserdef{sheet path}{started}{the letter x}[d()]
          {%
          myIfNoValueTF{#1}
          {%
          insertpath
          {--node[scale=sheetdotsize,inner sep=0pt]{.}++(sheetlength,0)}%
          }
          {%
          insertpath
          {%
          --node[scale=sheetdotsize,inner sep=0pt]{.}
          coordinate({#1})
          ++(sheetlength,0)
          }%
          }%
          }
          myparserdef{sheet path}{all}{the character ;}{myparserstate{final}outputpath}
          % <<<

          % sheet height and sheet length >>>
          pgfset
          {
          ,sheet height/.store in=sheetheight
          ,sheet height=1
          ,sheet length/.store in=sheetlength
          ,sheet length=1
          ,sheet dot size/.store in=sheetdotsize
          ,sheet dot size=4
          }
          %<<<

          begin{document}
          begin{tikzpicture}
          begin{scope}[thick, sheet height=0.75]
          sheet === ===d(sp1)=;
          sheet (0,-1) ==d(sp2)===ux =;
          sheet (0,-2) ==ux ===Dx =;
          sheet (0,-3) === ==== =;
          sheet (0,-4) === ===U(sp3)=;
          sheet (0,-5.5) ==x(b1) ===x(b2) =;
          end{scope}
          draw[dashed]
          (b2) -- (sp1)
          (b1) -- (sp2)
          ;
          end{tikzpicture}
          end{document}


          enter image description here






          share|improve this answer


























          • Wow ! This is a huge work. I'm impressed (like always I'm by the texperts ;)).

            – Kpym
            7 hours ago











          Your Answer








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          7 Answers
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          13














          This uses the same in and out trick as Skillmon and puts it into a style dip, which takes as arguments the horizontal position and the depth, where the sign decides whether the dip is a dip (minus) or a bump (plus). (Let me also mention that you do not need to do something like draw[<-] (0,0.35) -- (0,1.65) node[left, midway] {$f$};. If you name the nodes, you can just do draw[<-] (Y) -- (X) node[left, midway] {$f$}; and TikZ will make sure to shorten the arrow without you having to compute the coordinates.)



          documentclass[tikz,border=3.14mm]{standalone}
          usetikzlibrary{positioning}
          newcounter{dip}
          begin{document}
          begin{tikzpicture}[dip/.style args={#1/#2}{/utils/exec=stepcounter{dip},
          insert path={%
          coordinate (aux1) ({#1-abs(#2)},0) coordinate (aux2) ({#1+abs(#2)},0) coordinate (aux3)
          (aux1) -- (aux2|-aux1) to[out=0,in=180]
          ++({abs(#2)},#2) coordinate(dip-thevalue{dip}) to[out=0,in=180] (aux3|-aux1)
          }}]
          begin{scope}[thick,local bounding box=dips]
          draw (1,2.5) [dip=5.5cm/-2.5mm]-- (7,2.5);
          fill (dip-1) circle[radius=2pt] node[right=3pt]{$b=1$};
          draw (1,2) [dip/.list={2.5cm/-2.5mm,5.5cm/2.5mm}] -- (7,2);
          fill (dip-2) circle[radius=2pt] node[right=3pt]{$b=1$};
          draw (1,1.5) [dip/.list={2.5cm/2.5mm,5.5cm/-5mm}] -- (7,1.5);
          fill (dip-5) circle[radius=2pt] node[above right=0pt and 5pt]{$b=2$};
          draw (1,1) -- (7,1);
          draw (1,0.5) [dip=5.5cm/5mm] -- (7,0.5);
          end{scope}
          node[left=2pt of dips.west] (X) {$X$};
          draw (7,-0.5) -- (1,-0.5) node[left=2pt] (Y) {$Y$};
          draw[<-] (Y) -- (X) node[left, midway] {$f$};
          foreach X in {1,2}
          {
          fill (dip-X|-Y) circle[radius=2pt];
          draw[dashed] (dip-X|-Y) -- (dip-X|-0,2.75);
          }
          end{tikzpicture}
          end{document}


          enter image description here



          Just for fun: a variation for Skillmon.



          documentclass[tikz,border=3.14mm]{standalone}
          usetikzlibrary{positioning}
          newcounter{dip}
          begin{document}
          begin{tikzpicture}[dip/.style={/utils/exec=stepcounter{dip},
          insert path={%
          to[out=0,in=180]
          ++(0.25,#1) node[bullet](dip-thevalue{dip}){}
          to[out=0,in=180] ++(0.25,-1*#1)
          }},bullet/.style={circle,fill,inner sep=1.5pt}]
          begin{scope}[thick,local bounding box=dips]
          draw (1,2.5) -- (5.25,2.5) [dip=-2.5mm]-- (7,2.5);
          node[right=3pt of dip-1]{$b=1$};
          draw (1,2) -- (2.25,2) [dip=-2.5mm] -- (5.25,2) [dip=2.5mm] --(7,2);
          node[right=3pt of dip-2]{$b=1$};
          draw (1,1.5) -- (2.25,1.5) [dip=2.5mm] --(5.25,1.5) [dip=-5mm] -- (7,1.5);
          node[above right=-1.5pt and 5pt of dip-5]{$b=2$};
          draw (1,1) -- (7,1);
          draw (1,0.5) --(5.25,0.5) [dip=5mm] -- (7,0.5);
          end{scope}
          node[left=2pt of dips.west] (X) {$X$};
          draw (7,-0.5) -- (1,-0.5) node[left=2pt] (Y) {$Y$};
          draw[<-] (Y) -- (X) node[left, midway] {$f$};
          foreach X in {1,2}
          {
          draw[dashed] (dip-X|-Y) node[bullet]{} -- (dip-X|-0,2.75);
          }
          end{tikzpicture}
          end{document}


          enter image description here






          share|improve this answer


























          • Very nice automation. Just out of curiosity (coding TikZ is still something I'm not good at), is it possible to also draw the filled circles inside the dip style?

            – Skillmon
            yesterday






          • 1





            @Skillmon Yes, of course. E.g. dip/.style args={#1/#2}{/utils/exec=stepcounter{dip}, insert path={% coordinate (aux1) ({#1-abs(#2)},0) coordinate (aux2) ({#1+abs(#2)},0) coordinate (aux3) (aux1) -- (aux2|-aux1) to[out=0,in=180] ++({abs(#2)},#2) node[circle,fill,inner sep=1.5pt](dip-thevalue{dip}){} to[out=0,in=180] (aux3|-aux1) }}.

            – marmot
            yesterday
















          13














          This uses the same in and out trick as Skillmon and puts it into a style dip, which takes as arguments the horizontal position and the depth, where the sign decides whether the dip is a dip (minus) or a bump (plus). (Let me also mention that you do not need to do something like draw[<-] (0,0.35) -- (0,1.65) node[left, midway] {$f$};. If you name the nodes, you can just do draw[<-] (Y) -- (X) node[left, midway] {$f$}; and TikZ will make sure to shorten the arrow without you having to compute the coordinates.)



          documentclass[tikz,border=3.14mm]{standalone}
          usetikzlibrary{positioning}
          newcounter{dip}
          begin{document}
          begin{tikzpicture}[dip/.style args={#1/#2}{/utils/exec=stepcounter{dip},
          insert path={%
          coordinate (aux1) ({#1-abs(#2)},0) coordinate (aux2) ({#1+abs(#2)},0) coordinate (aux3)
          (aux1) -- (aux2|-aux1) to[out=0,in=180]
          ++({abs(#2)},#2) coordinate(dip-thevalue{dip}) to[out=0,in=180] (aux3|-aux1)
          }}]
          begin{scope}[thick,local bounding box=dips]
          draw (1,2.5) [dip=5.5cm/-2.5mm]-- (7,2.5);
          fill (dip-1) circle[radius=2pt] node[right=3pt]{$b=1$};
          draw (1,2) [dip/.list={2.5cm/-2.5mm,5.5cm/2.5mm}] -- (7,2);
          fill (dip-2) circle[radius=2pt] node[right=3pt]{$b=1$};
          draw (1,1.5) [dip/.list={2.5cm/2.5mm,5.5cm/-5mm}] -- (7,1.5);
          fill (dip-5) circle[radius=2pt] node[above right=0pt and 5pt]{$b=2$};
          draw (1,1) -- (7,1);
          draw (1,0.5) [dip=5.5cm/5mm] -- (7,0.5);
          end{scope}
          node[left=2pt of dips.west] (X) {$X$};
          draw (7,-0.5) -- (1,-0.5) node[left=2pt] (Y) {$Y$};
          draw[<-] (Y) -- (X) node[left, midway] {$f$};
          foreach X in {1,2}
          {
          fill (dip-X|-Y) circle[radius=2pt];
          draw[dashed] (dip-X|-Y) -- (dip-X|-0,2.75);
          }
          end{tikzpicture}
          end{document}


          enter image description here



          Just for fun: a variation for Skillmon.



          documentclass[tikz,border=3.14mm]{standalone}
          usetikzlibrary{positioning}
          newcounter{dip}
          begin{document}
          begin{tikzpicture}[dip/.style={/utils/exec=stepcounter{dip},
          insert path={%
          to[out=0,in=180]
          ++(0.25,#1) node[bullet](dip-thevalue{dip}){}
          to[out=0,in=180] ++(0.25,-1*#1)
          }},bullet/.style={circle,fill,inner sep=1.5pt}]
          begin{scope}[thick,local bounding box=dips]
          draw (1,2.5) -- (5.25,2.5) [dip=-2.5mm]-- (7,2.5);
          node[right=3pt of dip-1]{$b=1$};
          draw (1,2) -- (2.25,2) [dip=-2.5mm] -- (5.25,2) [dip=2.5mm] --(7,2);
          node[right=3pt of dip-2]{$b=1$};
          draw (1,1.5) -- (2.25,1.5) [dip=2.5mm] --(5.25,1.5) [dip=-5mm] -- (7,1.5);
          node[above right=-1.5pt and 5pt of dip-5]{$b=2$};
          draw (1,1) -- (7,1);
          draw (1,0.5) --(5.25,0.5) [dip=5mm] -- (7,0.5);
          end{scope}
          node[left=2pt of dips.west] (X) {$X$};
          draw (7,-0.5) -- (1,-0.5) node[left=2pt] (Y) {$Y$};
          draw[<-] (Y) -- (X) node[left, midway] {$f$};
          foreach X in {1,2}
          {
          draw[dashed] (dip-X|-Y) node[bullet]{} -- (dip-X|-0,2.75);
          }
          end{tikzpicture}
          end{document}


          enter image description here






          share|improve this answer


























          • Very nice automation. Just out of curiosity (coding TikZ is still something I'm not good at), is it possible to also draw the filled circles inside the dip style?

            – Skillmon
            yesterday






          • 1





            @Skillmon Yes, of course. E.g. dip/.style args={#1/#2}{/utils/exec=stepcounter{dip}, insert path={% coordinate (aux1) ({#1-abs(#2)},0) coordinate (aux2) ({#1+abs(#2)},0) coordinate (aux3) (aux1) -- (aux2|-aux1) to[out=0,in=180] ++({abs(#2)},#2) node[circle,fill,inner sep=1.5pt](dip-thevalue{dip}){} to[out=0,in=180] (aux3|-aux1) }}.

            – marmot
            yesterday














          13












          13








          13







          This uses the same in and out trick as Skillmon and puts it into a style dip, which takes as arguments the horizontal position and the depth, where the sign decides whether the dip is a dip (minus) or a bump (plus). (Let me also mention that you do not need to do something like draw[<-] (0,0.35) -- (0,1.65) node[left, midway] {$f$};. If you name the nodes, you can just do draw[<-] (Y) -- (X) node[left, midway] {$f$}; and TikZ will make sure to shorten the arrow without you having to compute the coordinates.)



          documentclass[tikz,border=3.14mm]{standalone}
          usetikzlibrary{positioning}
          newcounter{dip}
          begin{document}
          begin{tikzpicture}[dip/.style args={#1/#2}{/utils/exec=stepcounter{dip},
          insert path={%
          coordinate (aux1) ({#1-abs(#2)},0) coordinate (aux2) ({#1+abs(#2)},0) coordinate (aux3)
          (aux1) -- (aux2|-aux1) to[out=0,in=180]
          ++({abs(#2)},#2) coordinate(dip-thevalue{dip}) to[out=0,in=180] (aux3|-aux1)
          }}]
          begin{scope}[thick,local bounding box=dips]
          draw (1,2.5) [dip=5.5cm/-2.5mm]-- (7,2.5);
          fill (dip-1) circle[radius=2pt] node[right=3pt]{$b=1$};
          draw (1,2) [dip/.list={2.5cm/-2.5mm,5.5cm/2.5mm}] -- (7,2);
          fill (dip-2) circle[radius=2pt] node[right=3pt]{$b=1$};
          draw (1,1.5) [dip/.list={2.5cm/2.5mm,5.5cm/-5mm}] -- (7,1.5);
          fill (dip-5) circle[radius=2pt] node[above right=0pt and 5pt]{$b=2$};
          draw (1,1) -- (7,1);
          draw (1,0.5) [dip=5.5cm/5mm] -- (7,0.5);
          end{scope}
          node[left=2pt of dips.west] (X) {$X$};
          draw (7,-0.5) -- (1,-0.5) node[left=2pt] (Y) {$Y$};
          draw[<-] (Y) -- (X) node[left, midway] {$f$};
          foreach X in {1,2}
          {
          fill (dip-X|-Y) circle[radius=2pt];
          draw[dashed] (dip-X|-Y) -- (dip-X|-0,2.75);
          }
          end{tikzpicture}
          end{document}


          enter image description here



          Just for fun: a variation for Skillmon.



          documentclass[tikz,border=3.14mm]{standalone}
          usetikzlibrary{positioning}
          newcounter{dip}
          begin{document}
          begin{tikzpicture}[dip/.style={/utils/exec=stepcounter{dip},
          insert path={%
          to[out=0,in=180]
          ++(0.25,#1) node[bullet](dip-thevalue{dip}){}
          to[out=0,in=180] ++(0.25,-1*#1)
          }},bullet/.style={circle,fill,inner sep=1.5pt}]
          begin{scope}[thick,local bounding box=dips]
          draw (1,2.5) -- (5.25,2.5) [dip=-2.5mm]-- (7,2.5);
          node[right=3pt of dip-1]{$b=1$};
          draw (1,2) -- (2.25,2) [dip=-2.5mm] -- (5.25,2) [dip=2.5mm] --(7,2);
          node[right=3pt of dip-2]{$b=1$};
          draw (1,1.5) -- (2.25,1.5) [dip=2.5mm] --(5.25,1.5) [dip=-5mm] -- (7,1.5);
          node[above right=-1.5pt and 5pt of dip-5]{$b=2$};
          draw (1,1) -- (7,1);
          draw (1,0.5) --(5.25,0.5) [dip=5mm] -- (7,0.5);
          end{scope}
          node[left=2pt of dips.west] (X) {$X$};
          draw (7,-0.5) -- (1,-0.5) node[left=2pt] (Y) {$Y$};
          draw[<-] (Y) -- (X) node[left, midway] {$f$};
          foreach X in {1,2}
          {
          draw[dashed] (dip-X|-Y) node[bullet]{} -- (dip-X|-0,2.75);
          }
          end{tikzpicture}
          end{document}


          enter image description here






          share|improve this answer















          This uses the same in and out trick as Skillmon and puts it into a style dip, which takes as arguments the horizontal position and the depth, where the sign decides whether the dip is a dip (minus) or a bump (plus). (Let me also mention that you do not need to do something like draw[<-] (0,0.35) -- (0,1.65) node[left, midway] {$f$};. If you name the nodes, you can just do draw[<-] (Y) -- (X) node[left, midway] {$f$}; and TikZ will make sure to shorten the arrow without you having to compute the coordinates.)



          documentclass[tikz,border=3.14mm]{standalone}
          usetikzlibrary{positioning}
          newcounter{dip}
          begin{document}
          begin{tikzpicture}[dip/.style args={#1/#2}{/utils/exec=stepcounter{dip},
          insert path={%
          coordinate (aux1) ({#1-abs(#2)},0) coordinate (aux2) ({#1+abs(#2)},0) coordinate (aux3)
          (aux1) -- (aux2|-aux1) to[out=0,in=180]
          ++({abs(#2)},#2) coordinate(dip-thevalue{dip}) to[out=0,in=180] (aux3|-aux1)
          }}]
          begin{scope}[thick,local bounding box=dips]
          draw (1,2.5) [dip=5.5cm/-2.5mm]-- (7,2.5);
          fill (dip-1) circle[radius=2pt] node[right=3pt]{$b=1$};
          draw (1,2) [dip/.list={2.5cm/-2.5mm,5.5cm/2.5mm}] -- (7,2);
          fill (dip-2) circle[radius=2pt] node[right=3pt]{$b=1$};
          draw (1,1.5) [dip/.list={2.5cm/2.5mm,5.5cm/-5mm}] -- (7,1.5);
          fill (dip-5) circle[radius=2pt] node[above right=0pt and 5pt]{$b=2$};
          draw (1,1) -- (7,1);
          draw (1,0.5) [dip=5.5cm/5mm] -- (7,0.5);
          end{scope}
          node[left=2pt of dips.west] (X) {$X$};
          draw (7,-0.5) -- (1,-0.5) node[left=2pt] (Y) {$Y$};
          draw[<-] (Y) -- (X) node[left, midway] {$f$};
          foreach X in {1,2}
          {
          fill (dip-X|-Y) circle[radius=2pt];
          draw[dashed] (dip-X|-Y) -- (dip-X|-0,2.75);
          }
          end{tikzpicture}
          end{document}


          enter image description here



          Just for fun: a variation for Skillmon.



          documentclass[tikz,border=3.14mm]{standalone}
          usetikzlibrary{positioning}
          newcounter{dip}
          begin{document}
          begin{tikzpicture}[dip/.style={/utils/exec=stepcounter{dip},
          insert path={%
          to[out=0,in=180]
          ++(0.25,#1) node[bullet](dip-thevalue{dip}){}
          to[out=0,in=180] ++(0.25,-1*#1)
          }},bullet/.style={circle,fill,inner sep=1.5pt}]
          begin{scope}[thick,local bounding box=dips]
          draw (1,2.5) -- (5.25,2.5) [dip=-2.5mm]-- (7,2.5);
          node[right=3pt of dip-1]{$b=1$};
          draw (1,2) -- (2.25,2) [dip=-2.5mm] -- (5.25,2) [dip=2.5mm] --(7,2);
          node[right=3pt of dip-2]{$b=1$};
          draw (1,1.5) -- (2.25,1.5) [dip=2.5mm] --(5.25,1.5) [dip=-5mm] -- (7,1.5);
          node[above right=-1.5pt and 5pt of dip-5]{$b=2$};
          draw (1,1) -- (7,1);
          draw (1,0.5) --(5.25,0.5) [dip=5mm] -- (7,0.5);
          end{scope}
          node[left=2pt of dips.west] (X) {$X$};
          draw (7,-0.5) -- (1,-0.5) node[left=2pt] (Y) {$Y$};
          draw[<-] (Y) -- (X) node[left, midway] {$f$};
          foreach X in {1,2}
          {
          draw[dashed] (dip-X|-Y) node[bullet]{} -- (dip-X|-0,2.75);
          }
          end{tikzpicture}
          end{document}


          enter image description here







          share|improve this answer














          share|improve this answer



          share|improve this answer








          edited yesterday

























          answered 2 days ago









          marmotmarmot

          111k5140264




          111k5140264













          • Very nice automation. Just out of curiosity (coding TikZ is still something I'm not good at), is it possible to also draw the filled circles inside the dip style?

            – Skillmon
            yesterday






          • 1





            @Skillmon Yes, of course. E.g. dip/.style args={#1/#2}{/utils/exec=stepcounter{dip}, insert path={% coordinate (aux1) ({#1-abs(#2)},0) coordinate (aux2) ({#1+abs(#2)},0) coordinate (aux3) (aux1) -- (aux2|-aux1) to[out=0,in=180] ++({abs(#2)},#2) node[circle,fill,inner sep=1.5pt](dip-thevalue{dip}){} to[out=0,in=180] (aux3|-aux1) }}.

            – marmot
            yesterday



















          • Very nice automation. Just out of curiosity (coding TikZ is still something I'm not good at), is it possible to also draw the filled circles inside the dip style?

            – Skillmon
            yesterday






          • 1





            @Skillmon Yes, of course. E.g. dip/.style args={#1/#2}{/utils/exec=stepcounter{dip}, insert path={% coordinate (aux1) ({#1-abs(#2)},0) coordinate (aux2) ({#1+abs(#2)},0) coordinate (aux3) (aux1) -- (aux2|-aux1) to[out=0,in=180] ++({abs(#2)},#2) node[circle,fill,inner sep=1.5pt](dip-thevalue{dip}){} to[out=0,in=180] (aux3|-aux1) }}.

            – marmot
            yesterday

















          Very nice automation. Just out of curiosity (coding TikZ is still something I'm not good at), is it possible to also draw the filled circles inside the dip style?

          – Skillmon
          yesterday





          Very nice automation. Just out of curiosity (coding TikZ is still something I'm not good at), is it possible to also draw the filled circles inside the dip style?

          – Skillmon
          yesterday




          1




          1





          @Skillmon Yes, of course. E.g. dip/.style args={#1/#2}{/utils/exec=stepcounter{dip}, insert path={% coordinate (aux1) ({#1-abs(#2)},0) coordinate (aux2) ({#1+abs(#2)},0) coordinate (aux3) (aux1) -- (aux2|-aux1) to[out=0,in=180] ++({abs(#2)},#2) node[circle,fill,inner sep=1.5pt](dip-thevalue{dip}){} to[out=0,in=180] (aux3|-aux1) }}.

          – marmot
          yesterday





          @Skillmon Yes, of course. E.g. dip/.style args={#1/#2}{/utils/exec=stepcounter{dip}, insert path={% coordinate (aux1) ({#1-abs(#2)},0) coordinate (aux2) ({#1+abs(#2)},0) coordinate (aux3) (aux1) -- (aux2|-aux1) to[out=0,in=180] ++({abs(#2)},#2) node[circle,fill,inner sep=1.5pt](dip-thevalue{dip}){} to[out=0,in=180] (aux3|-aux1) }}.

          – marmot
          yesterday











          11














          The following is a pretty manual way to do this. I only did it for the first two lines, I hope you can apply it to the other occurrences. It uses the in and out keys of the to path construction:



          documentclass[tikz]{standalone}

          begin{document}
          begin{tikzpicture}
          draw (0,0) node {$Y$};
          draw (0,2) node {$X$};
          draw[<-] (0,0.35) -- (0,1.65) node[left, midway] {$f$};
          draw[thick] (1,2.5) -- (7,2.5) coordinate(a);
          draw[thick] (1,2) -- (7,2) coordinate(b);
          draw[thick] (1,1.5) -- (7,1.5) coordinate(c);
          draw[thick] (1,0) -- (7,0) coordinate(d);
          draw[thick]
          (a) ++(.25,-.25) coordinate(ab) to[out=180,in=0] (a)
          (ab) to[out=180,in=0] (b)
          (ab) to[out=0,in=180] ++(.25,.25)
          (ab) to[out=0,in=180] ++(.25,-.25)
          ;
          filldraw
          (ab) circle(.05)
          ;
          end{tikzpicture}
          end{document}


          enter image description here






          share|improve this answer






























            11














            The following is a pretty manual way to do this. I only did it for the first two lines, I hope you can apply it to the other occurrences. It uses the in and out keys of the to path construction:



            documentclass[tikz]{standalone}

            begin{document}
            begin{tikzpicture}
            draw (0,0) node {$Y$};
            draw (0,2) node {$X$};
            draw[<-] (0,0.35) -- (0,1.65) node[left, midway] {$f$};
            draw[thick] (1,2.5) -- (7,2.5) coordinate(a);
            draw[thick] (1,2) -- (7,2) coordinate(b);
            draw[thick] (1,1.5) -- (7,1.5) coordinate(c);
            draw[thick] (1,0) -- (7,0) coordinate(d);
            draw[thick]
            (a) ++(.25,-.25) coordinate(ab) to[out=180,in=0] (a)
            (ab) to[out=180,in=0] (b)
            (ab) to[out=0,in=180] ++(.25,.25)
            (ab) to[out=0,in=180] ++(.25,-.25)
            ;
            filldraw
            (ab) circle(.05)
            ;
            end{tikzpicture}
            end{document}


            enter image description here






            share|improve this answer




























              11












              11








              11







              The following is a pretty manual way to do this. I only did it for the first two lines, I hope you can apply it to the other occurrences. It uses the in and out keys of the to path construction:



              documentclass[tikz]{standalone}

              begin{document}
              begin{tikzpicture}
              draw (0,0) node {$Y$};
              draw (0,2) node {$X$};
              draw[<-] (0,0.35) -- (0,1.65) node[left, midway] {$f$};
              draw[thick] (1,2.5) -- (7,2.5) coordinate(a);
              draw[thick] (1,2) -- (7,2) coordinate(b);
              draw[thick] (1,1.5) -- (7,1.5) coordinate(c);
              draw[thick] (1,0) -- (7,0) coordinate(d);
              draw[thick]
              (a) ++(.25,-.25) coordinate(ab) to[out=180,in=0] (a)
              (ab) to[out=180,in=0] (b)
              (ab) to[out=0,in=180] ++(.25,.25)
              (ab) to[out=0,in=180] ++(.25,-.25)
              ;
              filldraw
              (ab) circle(.05)
              ;
              end{tikzpicture}
              end{document}


              enter image description here






              share|improve this answer















              The following is a pretty manual way to do this. I only did it for the first two lines, I hope you can apply it to the other occurrences. It uses the in and out keys of the to path construction:



              documentclass[tikz]{standalone}

              begin{document}
              begin{tikzpicture}
              draw (0,0) node {$Y$};
              draw (0,2) node {$X$};
              draw[<-] (0,0.35) -- (0,1.65) node[left, midway] {$f$};
              draw[thick] (1,2.5) -- (7,2.5) coordinate(a);
              draw[thick] (1,2) -- (7,2) coordinate(b);
              draw[thick] (1,1.5) -- (7,1.5) coordinate(c);
              draw[thick] (1,0) -- (7,0) coordinate(d);
              draw[thick]
              (a) ++(.25,-.25) coordinate(ab) to[out=180,in=0] (a)
              (ab) to[out=180,in=0] (b)
              (ab) to[out=0,in=180] ++(.25,.25)
              (ab) to[out=0,in=180] ++(.25,-.25)
              ;
              filldraw
              (ab) circle(.05)
              ;
              end{tikzpicture}
              end{document}


              enter image description here







              share|improve this answer














              share|improve this answer



              share|improve this answer








              edited 2 days ago

























              answered 2 days ago









              SkillmonSkillmon

              23.8k12248




              23.8k12248























                  10














                  This is a proof of concept how to use parser library to define the following "language" :





                  • = stay at the same level


                  • u goes half up


                  • U goes one up


                  • d goes half down


                  • D goes one down


                  • x plot a (red) dot


                  • . end


                  Here is the code.



                  documentclass[tikz,border=7pt]{standalone}
                  usepgfmodule{parser}
                  % -----------------------------
                  % macro that add #1 to the current path when used inside pgfextra
                  definsertpath#1{tikzset{insert path={#1}}}
                  % define the parser "sheet path"
                  pgfparserdef{sheet path}{initial}{the character =}{insertpath{ -- ++(1, 0)}}
                  pgfparserdef{sheet path}{initial}{the letter u}{insertpath{ to[out=0,in=180] ++(1, .5)}}
                  pgfparserdef{sheet path}{initial}{the letter U}{insertpath{ to[out=0,in=180] ++(1, 1)}}
                  pgfparserdef{sheet path}{initial}{the letter d}{insertpath{ to[out=0,in=180] ++(1,-.5)}}
                  pgfparserdef{sheet path}{initial}{the letter D}{insertpath{ to[out=0,in=180] ++(1, -1)}}
                  pgfparserdef{sheet path}{initial}{the letter x}{insertpath{ node[red,scale=4]{.}}}
                  pgfparserdef{sheet path}{initial}{the character .}{pgfparserswitch{final}}
                  % the sheet interface macro
                  defsheet#1.{pgfextra{pgfparserparse{sheet path}#1.}}
                  % -----------------------------
                  begin{document}
                  tikzdraw[thick]
                  (0,-1) sheet======du=.
                  (0,-2) sheet==du==uxd=.
                  (0,-3) sheet==uxd==DU=.
                  (0,-4) sheet=========.
                  (0,-5) sheet======UxD=.;
                  end{document}


                  enter image description here






                  share|improve this answer



















                  • 3





                    +1, I didn't know parser, wow!

                    – CarLaTeX
                    yesterday
















                  10














                  This is a proof of concept how to use parser library to define the following "language" :





                  • = stay at the same level


                  • u goes half up


                  • U goes one up


                  • d goes half down


                  • D goes one down


                  • x plot a (red) dot


                  • . end


                  Here is the code.



                  documentclass[tikz,border=7pt]{standalone}
                  usepgfmodule{parser}
                  % -----------------------------
                  % macro that add #1 to the current path when used inside pgfextra
                  definsertpath#1{tikzset{insert path={#1}}}
                  % define the parser "sheet path"
                  pgfparserdef{sheet path}{initial}{the character =}{insertpath{ -- ++(1, 0)}}
                  pgfparserdef{sheet path}{initial}{the letter u}{insertpath{ to[out=0,in=180] ++(1, .5)}}
                  pgfparserdef{sheet path}{initial}{the letter U}{insertpath{ to[out=0,in=180] ++(1, 1)}}
                  pgfparserdef{sheet path}{initial}{the letter d}{insertpath{ to[out=0,in=180] ++(1,-.5)}}
                  pgfparserdef{sheet path}{initial}{the letter D}{insertpath{ to[out=0,in=180] ++(1, -1)}}
                  pgfparserdef{sheet path}{initial}{the letter x}{insertpath{ node[red,scale=4]{.}}}
                  pgfparserdef{sheet path}{initial}{the character .}{pgfparserswitch{final}}
                  % the sheet interface macro
                  defsheet#1.{pgfextra{pgfparserparse{sheet path}#1.}}
                  % -----------------------------
                  begin{document}
                  tikzdraw[thick]
                  (0,-1) sheet======du=.
                  (0,-2) sheet==du==uxd=.
                  (0,-3) sheet==uxd==DU=.
                  (0,-4) sheet=========.
                  (0,-5) sheet======UxD=.;
                  end{document}


                  enter image description here






                  share|improve this answer



















                  • 3





                    +1, I didn't know parser, wow!

                    – CarLaTeX
                    yesterday














                  10












                  10








                  10







                  This is a proof of concept how to use parser library to define the following "language" :





                  • = stay at the same level


                  • u goes half up


                  • U goes one up


                  • d goes half down


                  • D goes one down


                  • x plot a (red) dot


                  • . end


                  Here is the code.



                  documentclass[tikz,border=7pt]{standalone}
                  usepgfmodule{parser}
                  % -----------------------------
                  % macro that add #1 to the current path when used inside pgfextra
                  definsertpath#1{tikzset{insert path={#1}}}
                  % define the parser "sheet path"
                  pgfparserdef{sheet path}{initial}{the character =}{insertpath{ -- ++(1, 0)}}
                  pgfparserdef{sheet path}{initial}{the letter u}{insertpath{ to[out=0,in=180] ++(1, .5)}}
                  pgfparserdef{sheet path}{initial}{the letter U}{insertpath{ to[out=0,in=180] ++(1, 1)}}
                  pgfparserdef{sheet path}{initial}{the letter d}{insertpath{ to[out=0,in=180] ++(1,-.5)}}
                  pgfparserdef{sheet path}{initial}{the letter D}{insertpath{ to[out=0,in=180] ++(1, -1)}}
                  pgfparserdef{sheet path}{initial}{the letter x}{insertpath{ node[red,scale=4]{.}}}
                  pgfparserdef{sheet path}{initial}{the character .}{pgfparserswitch{final}}
                  % the sheet interface macro
                  defsheet#1.{pgfextra{pgfparserparse{sheet path}#1.}}
                  % -----------------------------
                  begin{document}
                  tikzdraw[thick]
                  (0,-1) sheet======du=.
                  (0,-2) sheet==du==uxd=.
                  (0,-3) sheet==uxd==DU=.
                  (0,-4) sheet=========.
                  (0,-5) sheet======UxD=.;
                  end{document}


                  enter image description here






                  share|improve this answer













                  This is a proof of concept how to use parser library to define the following "language" :





                  • = stay at the same level


                  • u goes half up


                  • U goes one up


                  • d goes half down


                  • D goes one down


                  • x plot a (red) dot


                  • . end


                  Here is the code.



                  documentclass[tikz,border=7pt]{standalone}
                  usepgfmodule{parser}
                  % -----------------------------
                  % macro that add #1 to the current path when used inside pgfextra
                  definsertpath#1{tikzset{insert path={#1}}}
                  % define the parser "sheet path"
                  pgfparserdef{sheet path}{initial}{the character =}{insertpath{ -- ++(1, 0)}}
                  pgfparserdef{sheet path}{initial}{the letter u}{insertpath{ to[out=0,in=180] ++(1, .5)}}
                  pgfparserdef{sheet path}{initial}{the letter U}{insertpath{ to[out=0,in=180] ++(1, 1)}}
                  pgfparserdef{sheet path}{initial}{the letter d}{insertpath{ to[out=0,in=180] ++(1,-.5)}}
                  pgfparserdef{sheet path}{initial}{the letter D}{insertpath{ to[out=0,in=180] ++(1, -1)}}
                  pgfparserdef{sheet path}{initial}{the letter x}{insertpath{ node[red,scale=4]{.}}}
                  pgfparserdef{sheet path}{initial}{the character .}{pgfparserswitch{final}}
                  % the sheet interface macro
                  defsheet#1.{pgfextra{pgfparserparse{sheet path}#1.}}
                  % -----------------------------
                  begin{document}
                  tikzdraw[thick]
                  (0,-1) sheet======du=.
                  (0,-2) sheet==du==uxd=.
                  (0,-3) sheet==uxd==DU=.
                  (0,-4) sheet=========.
                  (0,-5) sheet======UxD=.;
                  end{document}


                  enter image description here







                  share|improve this answer












                  share|improve this answer



                  share|improve this answer










                  answered yesterday









                  KpymKpym

                  17k24090




                  17k24090








                  • 3





                    +1, I didn't know parser, wow!

                    – CarLaTeX
                    yesterday














                  • 3





                    +1, I didn't know parser, wow!

                    – CarLaTeX
                    yesterday








                  3




                  3





                  +1, I didn't know parser, wow!

                  – CarLaTeX
                  yesterday





                  +1, I didn't know parser, wow!

                  – CarLaTeX
                  yesterday











                  9














                  I think Bézier curves can do the task. It can make sure that the starting points and the ending points of all curves are placed with a consistent ratio.



                  documentclass[tikz]{standalone}
                  definnersep{.5em}
                  usetikzlibrary{patterns}
                  begin{document}
                  begin{tikzpicture}[y=baselineskip+2*innersep]
                  draw (0,0)--(6.5,0);
                  draw (0,1.5)--(6.5,1.5);
                  draw (0,1)--(4.75,1) .. controls (4.9,1) and (4.85,1.5) .. (5,1.5) .. controls (5.15,1.5) and (5.1,1) .. (5.25,1)--(6.5,1);
                  draw (0,2)--(1.25,2) .. controls (1.4,2) and (1.35,2.25) .. (1.5,2.25) .. controls (1.65,2.25) and (1.6,2) .. (1.75,2)--(4.75,2) .. controls (4.9,2) and (4.85,1.5) .. (5,1.5) .. controls (5.15,1.5) and (5.1,2) .. (5.25,2)--(6.5,2);
                  draw (0,2.5)--(1.25,2.5) .. controls (1.4,2.5) and (1.35,2.25) .. (1.5,2.25) .. controls (1.65,2.25) and (1.6,2.5) .. (1.75,2.5)--(4.75,2.5) .. controls (4.9,2.5) and (4.85,2.75) .. (5,2.75) .. controls (5.15,2.75) and (5.1,2.5) .. (5.25,2.5)--(6.5,2.5);
                  draw (0,3)--(4.75,3) .. controls (4.9,3) and (4.85,2.75) .. (5,2.75) .. controls (5.15,2.75) and (5.1,3) .. (5.25,3)--(6.5,3);
                  fill (1.5,2.25) circle (1.5pt) (5,1.5) circle (1.5pt) (5,2.75) circle (1.5pt) (1.5,0) circle (1.5pt) (5,0) circle (1.5pt);
                  draw[dashed] (1.5,0)--(1.5,3.25) (5,0)--(5,3.25);
                  draw (1.5,2.25) node[right=1ex] {$b=1$};
                  draw (5,1.75) node[right=1ex] {$b=2$};
                  draw (5,2.75) node[right=1ex] {$b=1$};
                  draw (-0.5,0) node (n) {$N$};
                  draw (-0.5,2.25) node (m) {$M$};
                  draw[-latex] (m)--(n) node[midway,left] {$f$};
                  end{tikzpicture}
                  end{document}


                  enter image description here






                  share|improve this answer




























                    9














                    I think Bézier curves can do the task. It can make sure that the starting points and the ending points of all curves are placed with a consistent ratio.



                    documentclass[tikz]{standalone}
                    definnersep{.5em}
                    usetikzlibrary{patterns}
                    begin{document}
                    begin{tikzpicture}[y=baselineskip+2*innersep]
                    draw (0,0)--(6.5,0);
                    draw (0,1.5)--(6.5,1.5);
                    draw (0,1)--(4.75,1) .. controls (4.9,1) and (4.85,1.5) .. (5,1.5) .. controls (5.15,1.5) and (5.1,1) .. (5.25,1)--(6.5,1);
                    draw (0,2)--(1.25,2) .. controls (1.4,2) and (1.35,2.25) .. (1.5,2.25) .. controls (1.65,2.25) and (1.6,2) .. (1.75,2)--(4.75,2) .. controls (4.9,2) and (4.85,1.5) .. (5,1.5) .. controls (5.15,1.5) and (5.1,2) .. (5.25,2)--(6.5,2);
                    draw (0,2.5)--(1.25,2.5) .. controls (1.4,2.5) and (1.35,2.25) .. (1.5,2.25) .. controls (1.65,2.25) and (1.6,2.5) .. (1.75,2.5)--(4.75,2.5) .. controls (4.9,2.5) and (4.85,2.75) .. (5,2.75) .. controls (5.15,2.75) and (5.1,2.5) .. (5.25,2.5)--(6.5,2.5);
                    draw (0,3)--(4.75,3) .. controls (4.9,3) and (4.85,2.75) .. (5,2.75) .. controls (5.15,2.75) and (5.1,3) .. (5.25,3)--(6.5,3);
                    fill (1.5,2.25) circle (1.5pt) (5,1.5) circle (1.5pt) (5,2.75) circle (1.5pt) (1.5,0) circle (1.5pt) (5,0) circle (1.5pt);
                    draw[dashed] (1.5,0)--(1.5,3.25) (5,0)--(5,3.25);
                    draw (1.5,2.25) node[right=1ex] {$b=1$};
                    draw (5,1.75) node[right=1ex] {$b=2$};
                    draw (5,2.75) node[right=1ex] {$b=1$};
                    draw (-0.5,0) node (n) {$N$};
                    draw (-0.5,2.25) node (m) {$M$};
                    draw[-latex] (m)--(n) node[midway,left] {$f$};
                    end{tikzpicture}
                    end{document}


                    enter image description here






                    share|improve this answer


























                      9












                      9








                      9







                      I think Bézier curves can do the task. It can make sure that the starting points and the ending points of all curves are placed with a consistent ratio.



                      documentclass[tikz]{standalone}
                      definnersep{.5em}
                      usetikzlibrary{patterns}
                      begin{document}
                      begin{tikzpicture}[y=baselineskip+2*innersep]
                      draw (0,0)--(6.5,0);
                      draw (0,1.5)--(6.5,1.5);
                      draw (0,1)--(4.75,1) .. controls (4.9,1) and (4.85,1.5) .. (5,1.5) .. controls (5.15,1.5) and (5.1,1) .. (5.25,1)--(6.5,1);
                      draw (0,2)--(1.25,2) .. controls (1.4,2) and (1.35,2.25) .. (1.5,2.25) .. controls (1.65,2.25) and (1.6,2) .. (1.75,2)--(4.75,2) .. controls (4.9,2) and (4.85,1.5) .. (5,1.5) .. controls (5.15,1.5) and (5.1,2) .. (5.25,2)--(6.5,2);
                      draw (0,2.5)--(1.25,2.5) .. controls (1.4,2.5) and (1.35,2.25) .. (1.5,2.25) .. controls (1.65,2.25) and (1.6,2.5) .. (1.75,2.5)--(4.75,2.5) .. controls (4.9,2.5) and (4.85,2.75) .. (5,2.75) .. controls (5.15,2.75) and (5.1,2.5) .. (5.25,2.5)--(6.5,2.5);
                      draw (0,3)--(4.75,3) .. controls (4.9,3) and (4.85,2.75) .. (5,2.75) .. controls (5.15,2.75) and (5.1,3) .. (5.25,3)--(6.5,3);
                      fill (1.5,2.25) circle (1.5pt) (5,1.5) circle (1.5pt) (5,2.75) circle (1.5pt) (1.5,0) circle (1.5pt) (5,0) circle (1.5pt);
                      draw[dashed] (1.5,0)--(1.5,3.25) (5,0)--(5,3.25);
                      draw (1.5,2.25) node[right=1ex] {$b=1$};
                      draw (5,1.75) node[right=1ex] {$b=2$};
                      draw (5,2.75) node[right=1ex] {$b=1$};
                      draw (-0.5,0) node (n) {$N$};
                      draw (-0.5,2.25) node (m) {$M$};
                      draw[-latex] (m)--(n) node[midway,left] {$f$};
                      end{tikzpicture}
                      end{document}


                      enter image description here






                      share|improve this answer













                      I think Bézier curves can do the task. It can make sure that the starting points and the ending points of all curves are placed with a consistent ratio.



                      documentclass[tikz]{standalone}
                      definnersep{.5em}
                      usetikzlibrary{patterns}
                      begin{document}
                      begin{tikzpicture}[y=baselineskip+2*innersep]
                      draw (0,0)--(6.5,0);
                      draw (0,1.5)--(6.5,1.5);
                      draw (0,1)--(4.75,1) .. controls (4.9,1) and (4.85,1.5) .. (5,1.5) .. controls (5.15,1.5) and (5.1,1) .. (5.25,1)--(6.5,1);
                      draw (0,2)--(1.25,2) .. controls (1.4,2) and (1.35,2.25) .. (1.5,2.25) .. controls (1.65,2.25) and (1.6,2) .. (1.75,2)--(4.75,2) .. controls (4.9,2) and (4.85,1.5) .. (5,1.5) .. controls (5.15,1.5) and (5.1,2) .. (5.25,2)--(6.5,2);
                      draw (0,2.5)--(1.25,2.5) .. controls (1.4,2.5) and (1.35,2.25) .. (1.5,2.25) .. controls (1.65,2.25) and (1.6,2.5) .. (1.75,2.5)--(4.75,2.5) .. controls (4.9,2.5) and (4.85,2.75) .. (5,2.75) .. controls (5.15,2.75) and (5.1,2.5) .. (5.25,2.5)--(6.5,2.5);
                      draw (0,3)--(4.75,3) .. controls (4.9,3) and (4.85,2.75) .. (5,2.75) .. controls (5.15,2.75) and (5.1,3) .. (5.25,3)--(6.5,3);
                      fill (1.5,2.25) circle (1.5pt) (5,1.5) circle (1.5pt) (5,2.75) circle (1.5pt) (1.5,0) circle (1.5pt) (5,0) circle (1.5pt);
                      draw[dashed] (1.5,0)--(1.5,3.25) (5,0)--(5,3.25);
                      draw (1.5,2.25) node[right=1ex] {$b=1$};
                      draw (5,1.75) node[right=1ex] {$b=2$};
                      draw (5,2.75) node[right=1ex] {$b=1$};
                      draw (-0.5,0) node (n) {$N$};
                      draw (-0.5,2.25) node (m) {$M$};
                      draw[-latex] (m)--(n) node[midway,left] {$f$};
                      end{tikzpicture}
                      end{document}


                      enter image description here







                      share|improve this answer












                      share|improve this answer



                      share|improve this answer










                      answered 2 days ago









                      JouleVJouleV

                      7,89222053




                      7,89222053























                          6














                          This is a proof of concept how to use plot[smooth] coordinates to do this.



                          documentclass[tikz,border=7pt]{standalone}
                          begin{document}
                          begin{tikzpicture}[yscale=.5,
                          sheet/.style={red,thick,smooth},
                          point/.style={insert path={node[scale=4]{.}}}]
                          % ---- sheets ----
                          foreach[count=i] pts in {
                          {(0, 0) (1, 0) (2, 0) (3, 0) (6, 0) (7,-1) (8, 0) (9, 0)},%
                          {(0, 0) (1, 0) (2,-1) (3, 0) (6, 0) (7, 1) (8, 0) (9, 0)},%
                          {(0, 0) (1, 0) (2, 1) (3, 0) (6, 0) (7,-2) (8, 0) (9, 0)},%
                          {(0, 0) (1, 0) (2, 0) (3, 0) (6, 0) (7, 0) (8, 0) (9, 0)},%
                          {(0, 0) (1, 0) (2, 0) (3, 0) (6, 0) (7, 2) (8, 0) (9, 0)},%
                          {(0,0)},%
                          {(0, 0) (9, 0)}%
                          }{
                          draw[yshift=-2*i cm,sheet] plot coordinates {pts};
                          }
                          % ---- singular points and labels ----
                          path
                          (2,-5) [point] (3,-5) node{$b=1$}
                          (7,-3) [point] (8,-3) node{$b=1$}
                          (7,-8) [point] (8,-7.5) node{$b=2$}
                          ;
                          % ---- vertical lines ----
                          draw[dashed]
                          (2,0) -- +(0,-14) [point]
                          (7,0) -- +(0,-14) [point]
                          ;
                          end{tikzpicture}
                          end{document}


                          enter image description here






                          share|improve this answer




























                            6














                            This is a proof of concept how to use plot[smooth] coordinates to do this.



                            documentclass[tikz,border=7pt]{standalone}
                            begin{document}
                            begin{tikzpicture}[yscale=.5,
                            sheet/.style={red,thick,smooth},
                            point/.style={insert path={node[scale=4]{.}}}]
                            % ---- sheets ----
                            foreach[count=i] pts in {
                            {(0, 0) (1, 0) (2, 0) (3, 0) (6, 0) (7,-1) (8, 0) (9, 0)},%
                            {(0, 0) (1, 0) (2,-1) (3, 0) (6, 0) (7, 1) (8, 0) (9, 0)},%
                            {(0, 0) (1, 0) (2, 1) (3, 0) (6, 0) (7,-2) (8, 0) (9, 0)},%
                            {(0, 0) (1, 0) (2, 0) (3, 0) (6, 0) (7, 0) (8, 0) (9, 0)},%
                            {(0, 0) (1, 0) (2, 0) (3, 0) (6, 0) (7, 2) (8, 0) (9, 0)},%
                            {(0,0)},%
                            {(0, 0) (9, 0)}%
                            }{
                            draw[yshift=-2*i cm,sheet] plot coordinates {pts};
                            }
                            % ---- singular points and labels ----
                            path
                            (2,-5) [point] (3,-5) node{$b=1$}
                            (7,-3) [point] (8,-3) node{$b=1$}
                            (7,-8) [point] (8,-7.5) node{$b=2$}
                            ;
                            % ---- vertical lines ----
                            draw[dashed]
                            (2,0) -- +(0,-14) [point]
                            (7,0) -- +(0,-14) [point]
                            ;
                            end{tikzpicture}
                            end{document}


                            enter image description here






                            share|improve this answer


























                              6












                              6








                              6







                              This is a proof of concept how to use plot[smooth] coordinates to do this.



                              documentclass[tikz,border=7pt]{standalone}
                              begin{document}
                              begin{tikzpicture}[yscale=.5,
                              sheet/.style={red,thick,smooth},
                              point/.style={insert path={node[scale=4]{.}}}]
                              % ---- sheets ----
                              foreach[count=i] pts in {
                              {(0, 0) (1, 0) (2, 0) (3, 0) (6, 0) (7,-1) (8, 0) (9, 0)},%
                              {(0, 0) (1, 0) (2,-1) (3, 0) (6, 0) (7, 1) (8, 0) (9, 0)},%
                              {(0, 0) (1, 0) (2, 1) (3, 0) (6, 0) (7,-2) (8, 0) (9, 0)},%
                              {(0, 0) (1, 0) (2, 0) (3, 0) (6, 0) (7, 0) (8, 0) (9, 0)},%
                              {(0, 0) (1, 0) (2, 0) (3, 0) (6, 0) (7, 2) (8, 0) (9, 0)},%
                              {(0,0)},%
                              {(0, 0) (9, 0)}%
                              }{
                              draw[yshift=-2*i cm,sheet] plot coordinates {pts};
                              }
                              % ---- singular points and labels ----
                              path
                              (2,-5) [point] (3,-5) node{$b=1$}
                              (7,-3) [point] (8,-3) node{$b=1$}
                              (7,-8) [point] (8,-7.5) node{$b=2$}
                              ;
                              % ---- vertical lines ----
                              draw[dashed]
                              (2,0) -- +(0,-14) [point]
                              (7,0) -- +(0,-14) [point]
                              ;
                              end{tikzpicture}
                              end{document}


                              enter image description here






                              share|improve this answer













                              This is a proof of concept how to use plot[smooth] coordinates to do this.



                              documentclass[tikz,border=7pt]{standalone}
                              begin{document}
                              begin{tikzpicture}[yscale=.5,
                              sheet/.style={red,thick,smooth},
                              point/.style={insert path={node[scale=4]{.}}}]
                              % ---- sheets ----
                              foreach[count=i] pts in {
                              {(0, 0) (1, 0) (2, 0) (3, 0) (6, 0) (7,-1) (8, 0) (9, 0)},%
                              {(0, 0) (1, 0) (2,-1) (3, 0) (6, 0) (7, 1) (8, 0) (9, 0)},%
                              {(0, 0) (1, 0) (2, 1) (3, 0) (6, 0) (7,-2) (8, 0) (9, 0)},%
                              {(0, 0) (1, 0) (2, 0) (3, 0) (6, 0) (7, 0) (8, 0) (9, 0)},%
                              {(0, 0) (1, 0) (2, 0) (3, 0) (6, 0) (7, 2) (8, 0) (9, 0)},%
                              {(0,0)},%
                              {(0, 0) (9, 0)}%
                              }{
                              draw[yshift=-2*i cm,sheet] plot coordinates {pts};
                              }
                              % ---- singular points and labels ----
                              path
                              (2,-5) [point] (3,-5) node{$b=1$}
                              (7,-3) [point] (8,-3) node{$b=1$}
                              (7,-8) [point] (8,-7.5) node{$b=2$}
                              ;
                              % ---- vertical lines ----
                              draw[dashed]
                              (2,0) -- +(0,-14) [point]
                              (7,0) -- +(0,-14) [point]
                              ;
                              end{tikzpicture}
                              end{document}


                              enter image description here







                              share|improve this answer












                              share|improve this answer



                              share|improve this answer










                              answered yesterday









                              KpymKpym

                              17k24090




                              17k24090























                                  5














                                  This is a proof of concept how to use turtle library to define the following "moves" :





                                  • up make an up bump


                                  • up* make an up bump with (red) dot


                                  • dn make a down bump


                                  • dn* make a down bump with (red) dot


                                  • * put a (red) dot


                                  documentclass[tikz,border=7pt]{standalone}
                                  usetikzlibrary{turtle}
                                  tikzset{
                                  turtle/.cd,
                                  how/.style={out=0,in=180},
                                  home/.append style=right,
                                  */.style={/tikz/insert path={node[red,scale=4]{.}}},
                                  forward/.default=1.4142135,
                                  up/.style={left=45,forward,right,forward,left=45},
                                  up*/.style={left=45,forward,*,right,forward,left=45},
                                  dn/.style={right=45,forward,left,forward,right=45},
                                  dn*/.style={right=45,forward,*,left,forward,right=45},
                                  next/.style={/tikz/yshift=-1cm}
                                  }

                                  begin{document}
                                  tikz
                                  draw[thick]
                                  [turtle={home,fd,fd,fd,fd,fd,fd,dn,fd},next,next]
                                  [turtle={home,fd,fd,dn,fd,fd,up*,fd},next,next]
                                  [turtle={home,fd,fd,up*,fd,fd,dn,fd},next]
                                  [turtle={home,fd,fd,fd,fd,fd,fd,fd,fd,fd},next]
                                  [turtle={home,fd,fd,fd,fd,fd,fd,up*,fd}]
                                  ;
                                  end{document}


                                  enter image description here






                                  share|improve this answer




























                                    5














                                    This is a proof of concept how to use turtle library to define the following "moves" :





                                    • up make an up bump


                                    • up* make an up bump with (red) dot


                                    • dn make a down bump


                                    • dn* make a down bump with (red) dot


                                    • * put a (red) dot


                                    documentclass[tikz,border=7pt]{standalone}
                                    usetikzlibrary{turtle}
                                    tikzset{
                                    turtle/.cd,
                                    how/.style={out=0,in=180},
                                    home/.append style=right,
                                    */.style={/tikz/insert path={node[red,scale=4]{.}}},
                                    forward/.default=1.4142135,
                                    up/.style={left=45,forward,right,forward,left=45},
                                    up*/.style={left=45,forward,*,right,forward,left=45},
                                    dn/.style={right=45,forward,left,forward,right=45},
                                    dn*/.style={right=45,forward,*,left,forward,right=45},
                                    next/.style={/tikz/yshift=-1cm}
                                    }

                                    begin{document}
                                    tikz
                                    draw[thick]
                                    [turtle={home,fd,fd,fd,fd,fd,fd,dn,fd},next,next]
                                    [turtle={home,fd,fd,dn,fd,fd,up*,fd},next,next]
                                    [turtle={home,fd,fd,up*,fd,fd,dn,fd},next]
                                    [turtle={home,fd,fd,fd,fd,fd,fd,fd,fd,fd},next]
                                    [turtle={home,fd,fd,fd,fd,fd,fd,up*,fd}]
                                    ;
                                    end{document}


                                    enter image description here






                                    share|improve this answer


























                                      5












                                      5








                                      5







                                      This is a proof of concept how to use turtle library to define the following "moves" :





                                      • up make an up bump


                                      • up* make an up bump with (red) dot


                                      • dn make a down bump


                                      • dn* make a down bump with (red) dot


                                      • * put a (red) dot


                                      documentclass[tikz,border=7pt]{standalone}
                                      usetikzlibrary{turtle}
                                      tikzset{
                                      turtle/.cd,
                                      how/.style={out=0,in=180},
                                      home/.append style=right,
                                      */.style={/tikz/insert path={node[red,scale=4]{.}}},
                                      forward/.default=1.4142135,
                                      up/.style={left=45,forward,right,forward,left=45},
                                      up*/.style={left=45,forward,*,right,forward,left=45},
                                      dn/.style={right=45,forward,left,forward,right=45},
                                      dn*/.style={right=45,forward,*,left,forward,right=45},
                                      next/.style={/tikz/yshift=-1cm}
                                      }

                                      begin{document}
                                      tikz
                                      draw[thick]
                                      [turtle={home,fd,fd,fd,fd,fd,fd,dn,fd},next,next]
                                      [turtle={home,fd,fd,dn,fd,fd,up*,fd},next,next]
                                      [turtle={home,fd,fd,up*,fd,fd,dn,fd},next]
                                      [turtle={home,fd,fd,fd,fd,fd,fd,fd,fd,fd},next]
                                      [turtle={home,fd,fd,fd,fd,fd,fd,up*,fd}]
                                      ;
                                      end{document}


                                      enter image description here






                                      share|improve this answer













                                      This is a proof of concept how to use turtle library to define the following "moves" :





                                      • up make an up bump


                                      • up* make an up bump with (red) dot


                                      • dn make a down bump


                                      • dn* make a down bump with (red) dot


                                      • * put a (red) dot


                                      documentclass[tikz,border=7pt]{standalone}
                                      usetikzlibrary{turtle}
                                      tikzset{
                                      turtle/.cd,
                                      how/.style={out=0,in=180},
                                      home/.append style=right,
                                      */.style={/tikz/insert path={node[red,scale=4]{.}}},
                                      forward/.default=1.4142135,
                                      up/.style={left=45,forward,right,forward,left=45},
                                      up*/.style={left=45,forward,*,right,forward,left=45},
                                      dn/.style={right=45,forward,left,forward,right=45},
                                      dn*/.style={right=45,forward,*,left,forward,right=45},
                                      next/.style={/tikz/yshift=-1cm}
                                      }

                                      begin{document}
                                      tikz
                                      draw[thick]
                                      [turtle={home,fd,fd,fd,fd,fd,fd,dn,fd},next,next]
                                      [turtle={home,fd,fd,dn,fd,fd,up*,fd},next,next]
                                      [turtle={home,fd,fd,up*,fd,fd,dn,fd},next]
                                      [turtle={home,fd,fd,fd,fd,fd,fd,fd,fd,fd},next]
                                      [turtle={home,fd,fd,fd,fd,fd,fd,up*,fd}]
                                      ;
                                      end{document}


                                      enter image description here







                                      share|improve this answer












                                      share|improve this answer



                                      share|improve this answer










                                      answered yesterday









                                      KpymKpym

                                      17k24090




                                      17k24090























                                          5














                                          Edit notes:




                                          • spaces can now be handled, but are ignored by default


                                          • alternative syntax for myparserdef added





                                          Inspired by Kpym's answer but thinking that the possibilities of pgfparser are insufficient, I wrote my own parser, that should be similar to pgf's, but allows the parsed elements to grab arguments. The following arguments are supported:





                                          • m a mandatory argument


                                          • r{<delim>} a mandatory argument delimited by <delim>


                                          • o an optional argument in brackets (you can test for it with myIfNoValueTF)


                                          • O{<default>} an optional argument defaulting to <default>


                                          • d<delim1><delim2> an optional argument delimited by <delim1> and <delim2> (you can test for it with myIfNoValueTF)


                                          • D<delim1><delim2>{<default>} an optional argument delimited by <delim1> and <delim2> defaulting to <default>


                                          • t<token> an optional token (you can test for it with myIfBooleanTF)


                                          Despite the fact that the argument names are inspired by xparse, none of them care for balanced delimiters (e.g., [[ab]] would not be grabbed as [ab], but as [ab with an orphaned ], so you'd have to use [{[ab]}], this is like the LaTeX2e behaviour). Also all arguments are long by nature unlike xparse where you'd need to specify that using +.



                                          You can define a parser using myparserdef{<name>}{<state>}{<meaning>}[<args>]{<code>}, with <name> the name of the parser, <state> the state, <meaning> the meaning of a token, <args> an argument string (built from the arguments listed above, up to 9 arguments are supported) and <code> the code which should be executed for that combination of <name>, <state> and <meaning>. You can switch states using myparserstate{<state>}, if you switch to final parsing is ended, the initial state is initial. All in all this is pretty similar to pgfparsers way of doing things. The biggest difference is, that my parser ignores blanks by default, however you can define an action for blanks with myparserdef{<name>}{<state>}{blank space}[<args>]{<code>}. Many consecutive blanks are considered as one.



                                          You can also use a different syntax for myparserdef namely: myparserdef{<name>}{<state>}<token>[<args>]{<code>} with <token> being a single token not surrounded by {} (spaces are ignored here, it is not checked whether <token> is really a single token, so be careful). In that case the same will be done as if you'd typed the meaning of the <token>, so myparserdef{foo}{bar}a{baz} does the same as myparserdef{foo}{bar}{the letter a}{baz}.



                                          A parser is executed using myparserrun{<name>}. A parser needs at least one rule, else an error is thrown.



                                          This parser system allows me to place coordinates inside of sheet, which was the main reason why I found pgfparser insufficient.



                                          I did all of this without using any packages, only LaTeX-Kernel macros, just for procrastinating reasons. Using for example xparse would shorten the code considerably.



                                          documentclass[tikz,border=7pt]{standalone}

                                          % my parser >>>
                                          makeatletter
                                          % logic helpers >>>
                                          longdefmyfi@An#1fi#2{fi}
                                          longdefmyfi@Ay#1fi#2{fi#2}
                                          longdefmyfi@Byfi#1{fi#1}
                                          longdefmyfi@BTbfi#1#2#3{fi#2}
                                          % <<<
                                          % mynewdef >>>
                                          @ifdefinablemyifundefTF%>>>
                                          {%
                                          defmyifundefTF#1%
                                          {%
                                          ifdefined#1%
                                          myfi@Ay
                                          else
                                          myfi@BTb
                                          fi
                                          {%
                                          ifx#1relax
                                          myfi@BTb
                                          fi
                                          @secondoftwo
                                          }%
                                          }%
                                          }%<<<
                                          @ifdefinablemynewdef%>>>
                                          {%
                                          protecteddefmynewdef{@ifnextchar[{mynewdef@a}{mynewdef@a}}%
                                          }%<<<
                                          @ifdefinablemynewdef@a%>>>
                                          {%
                                          longdefmynewdef@a[#1]#2#3#{mynewdef@b{#1}#2{#3}}%
                                          }%<<<
                                          @ifdefinablemynewdef@b%>>>
                                          {%
                                          protectedlongdefmynewdef@b#1#2#3#4%
                                          {%
                                          myifundefTF#2%
                                          {%
                                          #1def#2#3{#4}%
                                          }
                                          {%
                                          PackageError{my}{Command string#2space already defined}{}%
                                          }
                                          }%
                                          }%<<<
                                          mynewdefmyifcsundefTF#1%>>>
                                          {%
                                          ifcsname #1endcsname
                                          myfi@Ay
                                          else
                                          myfi@BTb
                                          fi
                                          {%
                                          expandafterifxcsname #1endcsnamerelax
                                          myfi@BTb
                                          fi
                                          @secondoftwo
                                          }%
                                          }%<<<
                                          % <<<
                                          % opt arg parsing >>>
                                          mynewdef[long]my@ifmark#1%>>>
                                          {%
                                          ifxmy@mark#1%
                                          myfi@BTb
                                          fi
                                          @secondoftwo
                                          }%<<<
                                          mynewdef[protectedlong]myoarg@oarg#1%>>>
                                          {%
                                          @ifnextchar[{myoarg@oarg@{#1}}{#1{my@mark}}%
                                          }%<<<
                                          mynewdef[long]myoarg@oarg@#1[#2]%>>>
                                          {%
                                          #1{#2}%
                                          }%<<<
                                          mynewdef[protectedlong]myoarg@Oarg#1#2%>>>
                                          {%
                                          @ifnextchar[{myoarg@oarg@{#2}}{#2{#1}}%
                                          }%<<<
                                          mynewdef[protectedlong]myoarg@darg#1#2#3%>>>
                                          {%
                                          longdefmyoarg@darg@##1#1##2#2{##1{##2}}%
                                          @ifnextchar#1{myoarg@darg@{#3}}{#3{my@mark}}%
                                          }%<<<
                                          mynewdef[protectedlong]myoarg@Darg#1#2#3#4%>>>
                                          {%
                                          longdefmyoarg@darg@##1#1##2#2{##1{##2}}%
                                          @ifnextchar#1{myoarg@darg@{#4}}{#4{#3}}%
                                          }%<<<
                                          % <<<
                                          % macros for string comparison >>>
                                          begingroupdef:{endgroupletmy@sptoken= }:
                                          mynewdefmy@mark{my@mark@if@you@see@this@report@it}
                                          mynewdefmy@stop{my@stop@if@you@see@this@report@it}
                                          mynewdefmyparser@final{final}
                                          mynewdefmyparser@noarg{noarg}
                                          mynewdefmyparser@blankspace{blank space}
                                          % <<<
                                          mynewdef[protected]myparserdef#1#2%>>>
                                          {%
                                          defmyparserdef@twoargs{{#1}{#2}}%
                                          myparserdef@a
                                          }%<<<
                                          mynewdef[protected]myparserdef@a%>>>
                                          {%
                                          futureletmyparserdef@argmyparserdef@b
                                          }%<<<
                                          mynewdefmyparserdef@b%>>>
                                          {%
                                          ifxmyparserdef@argmy@sptoken
                                          myfi@BTb
                                          fi
                                          @secondoftwo
                                          {myparserdef@gobble@space}
                                          {myparserdef@c}%
                                          }%<<<
                                          mynewdef[protected]myparserdef@gobble@space%>>>
                                          {%
                                          afterassignmentmyparserdef@a
                                          letmyparserdef@arg= % space after = to get spaces, too
                                          }%<<<
                                          mynewdef[protected]myparserdef@c#1%>>>
                                          {%
                                          ifxmyparserdef@argbgroup
                                          myfi@BTb
                                          fi
                                          @secondoftwo
                                          {%
                                          defmyparserdef@arg{#1}%
                                          ifxmyparser@blankspacemyparserdef@arg
                                          myfi@BTb
                                          fi
                                          @secondoftwo
                                          {expandaftermyparserdef@dmyparserdef@twoargs{blank space space}}
                                          {expandaftermyparserdef@dmyparserdef@twoargs{#1}}%
                                          }
                                          {expandaftermyparserdef@dmyparserdef@twoargs{meaningmyparserdef@arg}}%
                                          }%<<<
                                          mynewdef[long]myparserdef@d#1#2#3%>>>
                                          {%
                                          myoarg@oarg{myparserdef@e{#1}{#2}{#3}}%
                                          }%<<<
                                          mynewdef[protectedlong]myparserdef@e#1#2#3#4#5%>>>
                                          {%
                                          % if that is the first rule for the parser, define space to be a no-op
                                          myifcsundefTF{myparser@name{#1}}%
                                          {%
                                          expandafterdef
                                          csname myparser@name{#1} all blank space spacespace typeendcsname
                                          {noarg}%
                                          expandafterdef
                                          csname myparser@name{#1} all blank space spacespace codeendcsname
                                          {myparser@getnexttoken}%
                                          % use a macro as a flag that there is at least one parser rule defined
                                          expandafterdefcsnamemyparser@name{#1}endcsname{}%
                                          }
                                          {}%
                                          % check whether the optional argument was used
                                          my@ifmark{#4}
                                          {%
                                          % use a macro as flag that there is a rule for the specified state
                                          expandafterdefcsname myparser@name{#1} #2 #3 typeendcsname{noarg}%
                                          defmyparserdef@arg@count{0}%
                                          }
                                          {%
                                          edefmyparserdef@arg@count
                                          {thenumexprmyparserdef@argcount#4my@mark}%
                                          ifnummyparserdef@arg@count>9%
                                          PackageError{my}{Too many arguments for parser rule}
                                          {A maximum of 9 parameters is supported.}%
                                          else
                                          ifnummyparserdef@arg@count=0%
                                          expandafterdefcsname myparser@name{#1} #2 #3 typeendcsname
                                          {noarg}%
                                          else
                                          expandafterdefcsname myparser@name{#1} #2 #3 typeendcsname{#4}%
                                          fi
                                          fi
                                          }%
                                          % define what the code does
                                          expandafterdefcsname myparser@name{#1} #2 #3 codeendcsname{}%
                                          expandafterrenewcommandcsname myparser@name{#1} #2 #3 codeendcsname
                                          [myparserdef@arg@count]{#5myparser@getnexttoken}%
                                          }%<<<
                                          mynewdefmyparserdef@argcount#1%>>>
                                          {%
                                          ifxmy@mark#1%
                                          myfi@An
                                          else
                                          myfi@By
                                          fi
                                          {csname myparserdef@argcount@#1endcsname}%
                                          }%<<<
                                          mynewdefmyparserdef@argcount@m%>>>
                                          {%
                                          +1%
                                          myparserdef@argcount
                                          }%<<<
                                          mynewdefmyparserdef@argcount@o%>>>
                                          {%
                                          +1%
                                          myparserdef@argcount
                                          }%<<<
                                          mynewdefmyparserdef@argcount@O#1%>>>
                                          {%
                                          +1%
                                          myparserdef@argcount
                                          }%<<<
                                          mynewdefmyparserdef@argcount@d#1#2%>>>
                                          {%
                                          +1%
                                          myparserdef@argcount
                                          }%<<<
                                          mynewdefmyparserdef@argcount@D#1#2#3%>>>
                                          {%
                                          +1%
                                          myparserdef@argcount
                                          }%<<<
                                          mynewdefmyparserdef@argcount@r#1%>>>
                                          {%
                                          +1%
                                          myparserdef@argcount
                                          }%<<<
                                          mynewdefmyparserdef@argcount@t#1%>>>
                                          {%
                                          +1%
                                          myparserdef@argcount
                                          }%<<<
                                          mynewdefmyparser@name#1%>>>
                                          {%
                                          myparser #1%
                                          }%<<<
                                          mynewdefmyparser@rule#1%>>>
                                          {%
                                          myparser@currentspace #1space meaningmyparser@token
                                          }%<<<
                                          mynewdefmyparser@type#1%>>>
                                          {%
                                          myparser@rule{#1} type%
                                          }%<<<
                                          mynewdefmyparser@code#1%>>>
                                          {%
                                          myparser@rule{#1} code%
                                          }%<<<
                                          mynewdef[protected]myparserrun#1%>>>
                                          {%
                                          myifcsundefTF{myparser@name{#1}}
                                          {PackageError{my}{No parser named '#1' defined}{}}
                                          {%
                                          edefmyparser@current{myparser@name{#1}}%
                                          defmyparser@usersname{#1}%
                                          defmyparser@state{initial}%
                                          myparser@getnexttoken
                                          }%
                                          }%<<<
                                          mynewdef[protected]myparser@getnexttoken%>>>
                                          {%
                                          ifxmyparser@statemyparser@final
                                          myfi@An
                                          else
                                          myfi@By
                                          fi
                                          {%
                                          afterassignmentmyparser@getnexttoken@a
                                          letmyparser@token= % space after = to get spaces, too
                                          }%
                                          }%<<<
                                          mynewdef[protected]myparser@getnexttoken@a%>>>
                                          {%
                                          myifcsundefTF{myparser@type{myparser@state}}
                                          {%
                                          myifcsundefTF{myparser@type{all}}
                                          {%
                                          PackageError{my}
                                          {%
                                          No rule for parser 'myparser@usersname' in state
                                          'myparser@state' for 'meaningmyparser@token'.
                                          Ignoring token%
                                          }
                                          {}%
                                          myparser@getnexttoken
                                          }
                                          {myparser@handle{all}}%
                                          }
                                          {myparser@handle{myparser@state}}%
                                          }%<<<
                                          mynewdef[protected]myparser@handle#1%>>>
                                          {%
                                          expandafterifxcsnamemyparser@type{#1}endcsnamemyparser@noarg
                                          myfi@BTb
                                          fi
                                          @secondoftwo
                                          {csnamemyparser@code{#1}endcsname}
                                          {myparser@handle@args{#1}}%
                                          }%<<<
                                          mynewdef[protected]myparserstate#1%>>>
                                          {%
                                          defmyparser@state{#1}%
                                          }%<<<
                                          mynewdef[protected]myparser@handle@args#1%>>>
                                          {%
                                          defmyparser@stateorall{#1}%
                                          expandafterexpandafterexpandaftermyparser@handle@args@a
                                          csnamemyparser@type{#1}endcsnamemy@markmy@stop
                                          }%<<<
                                          mynewdefmyparser@handle@args@a%>>>
                                          {%
                                          myparser@handle@args@b{}%
                                          }%<<<
                                          mynewdef[long]myparser@handle@args@b#1#2#3my@stop%>>>
                                          {%
                                          my@ifmark{#2}
                                          {csnamemyparser@code{myparser@stateorall}endcsname#1}
                                          {%
                                          myifcsundefTF{myparser@handle@args@#2}
                                          {PackageError{my}{Unknown argument type '#2'}{}}
                                          {csname myparser@handle@args@#2endcsname{#1}{#3}}%
                                          }%
                                          }%<<<
                                          mynewdef[long]myparser@handle@args@c#1#2%>>>
                                          {%
                                          my@ifmark{#2}
                                          {csnamemyparser@code{myparser@stateorall}endcsname#1}
                                          {myparser@handle@args@b{#1}#2my@stop}%
                                          }%<<<
                                          mynewdef[long]myparser@handle@args@m#1#2#3%>>>
                                          {%
                                          myparser@handle@args@c{#1{#3}}{#2}%
                                          }%<<<
                                          mynewdef[protectedlong]myparser@handle@args@o#1#2%>>>
                                          {%
                                          myoarg@oarg{myparser@handle@args@m{#1}{#2}}%
                                          }%<<<
                                          mynewdef[long]myparser@handle@args@O#1#2%>>>
                                          {%
                                          myparser@handle@args@O@{#1}#2my@stop
                                          }%<<<
                                          mynewdef[protectedlong]myparser@handle@args@O@#1#2#3my@stop%>>>
                                          {%
                                          myoarg@Oarg{#2}{myparser@handle@args@m{#1}{#3}}%
                                          }%<<<
                                          mynewdef[long]myparser@handle@args@d#1#2%>>>
                                          {%
                                          myparser@handle@args@d@{#1}#2my@stop
                                          }%<<<
                                          mynewdef[protectedlong]myparser@handle@args@d@#1#2#3#4my@stop%>>>
                                          {%
                                          myoarg@darg{#2}{#3}{myparser@handle@args@m{#1}{#4}}%
                                          }%<<<
                                          mynewdef[long]myparser@handle@args@D#1#2%>>>
                                          {%
                                          myparser@handle@args@D@{#1}#2my@stop
                                          }%<<<
                                          mynewdef[protectedlong]myparser@handle@args@D@#1#2#3#4#5my@stop%>>>
                                          {%
                                          myoarg@Darg{#2}{#3}{#4}{myparser@handle@args@m{#1}{#5}}%
                                          }%<<<
                                          mynewdef[long]myparser@handle@args@r#1#2%>>>
                                          {%
                                          myparser@handle@args@r@a{#1}#2my@stop
                                          }%<<<
                                          mynewdef[protectedlong]myparser@handle@args@r@a#1#2#3my@stop%>>>
                                          {%
                                          defmyparser@handle@args@r@b##1#2{myparser@handle@args@c{#1{##1}}{#3}}%
                                          myparser@handle@args@r@b
                                          }%<<<
                                          mynewdef[long]myparser@handle@args@t#1#2%>>>
                                          {%
                                          myparser@handle@args@t@a{#1}#2my@stop
                                          }%<<<
                                          mynewdef[protectedlong]myparser@handle@args@t@a#1#2#3my@stop%>>>
                                          {%
                                          @ifnextchar#2%
                                          {@firstoftwo{myparser@handle@args@c{#1{my@mark}}{#3}}}
                                          {myparser@handle@args@c{#1{my@stop}}{#3}}%
                                          }%<<<
                                          letmyIfNoValueTFmy@ifmark
                                          letmyIfBooleanTFmy@ifmark
                                          makeatother
                                          % <<<

                                          % the sheet path parser >>>
                                          makeatletter
                                          definsertpath#1{edefsheetpath@{unexpandedexpandafter{sheetpath@#1}}}
                                          defsheetpathcurve#1#2#3#4%
                                          {%
                                          to[out=0,in=180] ++({.5*sheetlength},{#1*sheetheight})
                                          myIfBooleanTF{#3}{}{node[scale=sheetdotsize,inner sep=0pt]{.}}
                                          myIfNoValueTF{#4}{}{coordinate({#4})}
                                          to[out=0,in=180] ++({.5*sheetlength},{#2*sheetheight})
                                          }
                                          defoutputpath{drawsheetpath@;}
                                          defsheet{defsheetpath@{}myparserrun{sheet path}}
                                          makeatother
                                          myparserdef{sheet path}{initial}{the character (}[r,r)]
                                          {insertpath{({#1},{#2*sheetheight})}myparserstate{started}}
                                          myparserdef{sheet path}{initial}{the character =}
                                          {insertpath{(0,0)--++(sheetlength,0)}myparserstate{started}}
                                          myparserdef{sheet path}{started}{the character (}[r)]
                                          {insertpath{coordinate({#1})}}
                                          myparserdef{sheet path}{started}{the character =}
                                          {insertpath{--++(sheetlength,0)}}
                                          myparserdef{sheet path}{started}{the letter u}[txd()]
                                          {insertpath{sheetpathcurve{.5}{-.5}{#1}{#2}}}
                                          myparserdef{sheet path}{started}{the letter U}[txd()]
                                          {insertpath{sheetpathcurve{1}{-1}{#1}{#2}}}
                                          myparserdef{sheet path}{started}{the letter d}[txd()]
                                          {insertpath{sheetpathcurve{-.5}{.5}{#1}{#2}}}
                                          myparserdef{sheet path}{started}{the letter D}[txd()]
                                          {insertpath{sheetpathcurve{-1}{1}{#1}{#2}}}
                                          % making '.' a no-op, that way we can use it to end the search for an optional
                                          % argument for instance
                                          myparserdef{sheet path}{started} .{}
                                          myparserdef{sheet path}{started}{the letter x}[d()]
                                          {%
                                          myIfNoValueTF{#1}
                                          {%
                                          insertpath
                                          {--node[scale=sheetdotsize,inner sep=0pt]{.}++(sheetlength,0)}%
                                          }
                                          {%
                                          insertpath
                                          {%
                                          --node[scale=sheetdotsize,inner sep=0pt]{.}
                                          coordinate({#1})
                                          ++(sheetlength,0)
                                          }%
                                          }%
                                          }
                                          myparserdef{sheet path}{all}{the character ;}{myparserstate{final}outputpath}
                                          % <<<

                                          % sheet height and sheet length >>>
                                          pgfset
                                          {
                                          ,sheet height/.store in=sheetheight
                                          ,sheet height=1
                                          ,sheet length/.store in=sheetlength
                                          ,sheet length=1
                                          ,sheet dot size/.store in=sheetdotsize
                                          ,sheet dot size=4
                                          }
                                          %<<<

                                          begin{document}
                                          begin{tikzpicture}
                                          begin{scope}[thick, sheet height=0.75]
                                          sheet === ===d(sp1)=;
                                          sheet (0,-1) ==d(sp2)===ux =;
                                          sheet (0,-2) ==ux ===Dx =;
                                          sheet (0,-3) === ==== =;
                                          sheet (0,-4) === ===U(sp3)=;
                                          sheet (0,-5.5) ==x(b1) ===x(b2) =;
                                          end{scope}
                                          draw[dashed]
                                          (b2) -- (sp1)
                                          (b1) -- (sp2)
                                          ;
                                          end{tikzpicture}
                                          end{document}


                                          enter image description here






                                          share|improve this answer


























                                          • Wow ! This is a huge work. I'm impressed (like always I'm by the texperts ;)).

                                            – Kpym
                                            7 hours ago
















                                          5














                                          Edit notes:




                                          • spaces can now be handled, but are ignored by default


                                          • alternative syntax for myparserdef added





                                          Inspired by Kpym's answer but thinking that the possibilities of pgfparser are insufficient, I wrote my own parser, that should be similar to pgf's, but allows the parsed elements to grab arguments. The following arguments are supported:





                                          • m a mandatory argument


                                          • r{<delim>} a mandatory argument delimited by <delim>


                                          • o an optional argument in brackets (you can test for it with myIfNoValueTF)


                                          • O{<default>} an optional argument defaulting to <default>


                                          • d<delim1><delim2> an optional argument delimited by <delim1> and <delim2> (you can test for it with myIfNoValueTF)


                                          • D<delim1><delim2>{<default>} an optional argument delimited by <delim1> and <delim2> defaulting to <default>


                                          • t<token> an optional token (you can test for it with myIfBooleanTF)


                                          Despite the fact that the argument names are inspired by xparse, none of them care for balanced delimiters (e.g., [[ab]] would not be grabbed as [ab], but as [ab with an orphaned ], so you'd have to use [{[ab]}], this is like the LaTeX2e behaviour). Also all arguments are long by nature unlike xparse where you'd need to specify that using +.



                                          You can define a parser using myparserdef{<name>}{<state>}{<meaning>}[<args>]{<code>}, with <name> the name of the parser, <state> the state, <meaning> the meaning of a token, <args> an argument string (built from the arguments listed above, up to 9 arguments are supported) and <code> the code which should be executed for that combination of <name>, <state> and <meaning>. You can switch states using myparserstate{<state>}, if you switch to final parsing is ended, the initial state is initial. All in all this is pretty similar to pgfparsers way of doing things. The biggest difference is, that my parser ignores blanks by default, however you can define an action for blanks with myparserdef{<name>}{<state>}{blank space}[<args>]{<code>}. Many consecutive blanks are considered as one.



                                          You can also use a different syntax for myparserdef namely: myparserdef{<name>}{<state>}<token>[<args>]{<code>} with <token> being a single token not surrounded by {} (spaces are ignored here, it is not checked whether <token> is really a single token, so be careful). In that case the same will be done as if you'd typed the meaning of the <token>, so myparserdef{foo}{bar}a{baz} does the same as myparserdef{foo}{bar}{the letter a}{baz}.



                                          A parser is executed using myparserrun{<name>}. A parser needs at least one rule, else an error is thrown.



                                          This parser system allows me to place coordinates inside of sheet, which was the main reason why I found pgfparser insufficient.



                                          I did all of this without using any packages, only LaTeX-Kernel macros, just for procrastinating reasons. Using for example xparse would shorten the code considerably.



                                          documentclass[tikz,border=7pt]{standalone}

                                          % my parser >>>
                                          makeatletter
                                          % logic helpers >>>
                                          longdefmyfi@An#1fi#2{fi}
                                          longdefmyfi@Ay#1fi#2{fi#2}
                                          longdefmyfi@Byfi#1{fi#1}
                                          longdefmyfi@BTbfi#1#2#3{fi#2}
                                          % <<<
                                          % mynewdef >>>
                                          @ifdefinablemyifundefTF%>>>
                                          {%
                                          defmyifundefTF#1%
                                          {%
                                          ifdefined#1%
                                          myfi@Ay
                                          else
                                          myfi@BTb
                                          fi
                                          {%
                                          ifx#1relax
                                          myfi@BTb
                                          fi
                                          @secondoftwo
                                          }%
                                          }%
                                          }%<<<
                                          @ifdefinablemynewdef%>>>
                                          {%
                                          protecteddefmynewdef{@ifnextchar[{mynewdef@a}{mynewdef@a}}%
                                          }%<<<
                                          @ifdefinablemynewdef@a%>>>
                                          {%
                                          longdefmynewdef@a[#1]#2#3#{mynewdef@b{#1}#2{#3}}%
                                          }%<<<
                                          @ifdefinablemynewdef@b%>>>
                                          {%
                                          protectedlongdefmynewdef@b#1#2#3#4%
                                          {%
                                          myifundefTF#2%
                                          {%
                                          #1def#2#3{#4}%
                                          }
                                          {%
                                          PackageError{my}{Command string#2space already defined}{}%
                                          }
                                          }%
                                          }%<<<
                                          mynewdefmyifcsundefTF#1%>>>
                                          {%
                                          ifcsname #1endcsname
                                          myfi@Ay
                                          else
                                          myfi@BTb
                                          fi
                                          {%
                                          expandafterifxcsname #1endcsnamerelax
                                          myfi@BTb
                                          fi
                                          @secondoftwo
                                          }%
                                          }%<<<
                                          % <<<
                                          % opt arg parsing >>>
                                          mynewdef[long]my@ifmark#1%>>>
                                          {%
                                          ifxmy@mark#1%
                                          myfi@BTb
                                          fi
                                          @secondoftwo
                                          }%<<<
                                          mynewdef[protectedlong]myoarg@oarg#1%>>>
                                          {%
                                          @ifnextchar[{myoarg@oarg@{#1}}{#1{my@mark}}%
                                          }%<<<
                                          mynewdef[long]myoarg@oarg@#1[#2]%>>>
                                          {%
                                          #1{#2}%
                                          }%<<<
                                          mynewdef[protectedlong]myoarg@Oarg#1#2%>>>
                                          {%
                                          @ifnextchar[{myoarg@oarg@{#2}}{#2{#1}}%
                                          }%<<<
                                          mynewdef[protectedlong]myoarg@darg#1#2#3%>>>
                                          {%
                                          longdefmyoarg@darg@##1#1##2#2{##1{##2}}%
                                          @ifnextchar#1{myoarg@darg@{#3}}{#3{my@mark}}%
                                          }%<<<
                                          mynewdef[protectedlong]myoarg@Darg#1#2#3#4%>>>
                                          {%
                                          longdefmyoarg@darg@##1#1##2#2{##1{##2}}%
                                          @ifnextchar#1{myoarg@darg@{#4}}{#4{#3}}%
                                          }%<<<
                                          % <<<
                                          % macros for string comparison >>>
                                          begingroupdef:{endgroupletmy@sptoken= }:
                                          mynewdefmy@mark{my@mark@if@you@see@this@report@it}
                                          mynewdefmy@stop{my@stop@if@you@see@this@report@it}
                                          mynewdefmyparser@final{final}
                                          mynewdefmyparser@noarg{noarg}
                                          mynewdefmyparser@blankspace{blank space}
                                          % <<<
                                          mynewdef[protected]myparserdef#1#2%>>>
                                          {%
                                          defmyparserdef@twoargs{{#1}{#2}}%
                                          myparserdef@a
                                          }%<<<
                                          mynewdef[protected]myparserdef@a%>>>
                                          {%
                                          futureletmyparserdef@argmyparserdef@b
                                          }%<<<
                                          mynewdefmyparserdef@b%>>>
                                          {%
                                          ifxmyparserdef@argmy@sptoken
                                          myfi@BTb
                                          fi
                                          @secondoftwo
                                          {myparserdef@gobble@space}
                                          {myparserdef@c}%
                                          }%<<<
                                          mynewdef[protected]myparserdef@gobble@space%>>>
                                          {%
                                          afterassignmentmyparserdef@a
                                          letmyparserdef@arg= % space after = to get spaces, too
                                          }%<<<
                                          mynewdef[protected]myparserdef@c#1%>>>
                                          {%
                                          ifxmyparserdef@argbgroup
                                          myfi@BTb
                                          fi
                                          @secondoftwo
                                          {%
                                          defmyparserdef@arg{#1}%
                                          ifxmyparser@blankspacemyparserdef@arg
                                          myfi@BTb
                                          fi
                                          @secondoftwo
                                          {expandaftermyparserdef@dmyparserdef@twoargs{blank space space}}
                                          {expandaftermyparserdef@dmyparserdef@twoargs{#1}}%
                                          }
                                          {expandaftermyparserdef@dmyparserdef@twoargs{meaningmyparserdef@arg}}%
                                          }%<<<
                                          mynewdef[long]myparserdef@d#1#2#3%>>>
                                          {%
                                          myoarg@oarg{myparserdef@e{#1}{#2}{#3}}%
                                          }%<<<
                                          mynewdef[protectedlong]myparserdef@e#1#2#3#4#5%>>>
                                          {%
                                          % if that is the first rule for the parser, define space to be a no-op
                                          myifcsundefTF{myparser@name{#1}}%
                                          {%
                                          expandafterdef
                                          csname myparser@name{#1} all blank space spacespace typeendcsname
                                          {noarg}%
                                          expandafterdef
                                          csname myparser@name{#1} all blank space spacespace codeendcsname
                                          {myparser@getnexttoken}%
                                          % use a macro as a flag that there is at least one parser rule defined
                                          expandafterdefcsnamemyparser@name{#1}endcsname{}%
                                          }
                                          {}%
                                          % check whether the optional argument was used
                                          my@ifmark{#4}
                                          {%
                                          % use a macro as flag that there is a rule for the specified state
                                          expandafterdefcsname myparser@name{#1} #2 #3 typeendcsname{noarg}%
                                          defmyparserdef@arg@count{0}%
                                          }
                                          {%
                                          edefmyparserdef@arg@count
                                          {thenumexprmyparserdef@argcount#4my@mark}%
                                          ifnummyparserdef@arg@count>9%
                                          PackageError{my}{Too many arguments for parser rule}
                                          {A maximum of 9 parameters is supported.}%
                                          else
                                          ifnummyparserdef@arg@count=0%
                                          expandafterdefcsname myparser@name{#1} #2 #3 typeendcsname
                                          {noarg}%
                                          else
                                          expandafterdefcsname myparser@name{#1} #2 #3 typeendcsname{#4}%
                                          fi
                                          fi
                                          }%
                                          % define what the code does
                                          expandafterdefcsname myparser@name{#1} #2 #3 codeendcsname{}%
                                          expandafterrenewcommandcsname myparser@name{#1} #2 #3 codeendcsname
                                          [myparserdef@arg@count]{#5myparser@getnexttoken}%
                                          }%<<<
                                          mynewdefmyparserdef@argcount#1%>>>
                                          {%
                                          ifxmy@mark#1%
                                          myfi@An
                                          else
                                          myfi@By
                                          fi
                                          {csname myparserdef@argcount@#1endcsname}%
                                          }%<<<
                                          mynewdefmyparserdef@argcount@m%>>>
                                          {%
                                          +1%
                                          myparserdef@argcount
                                          }%<<<
                                          mynewdefmyparserdef@argcount@o%>>>
                                          {%
                                          +1%
                                          myparserdef@argcount
                                          }%<<<
                                          mynewdefmyparserdef@argcount@O#1%>>>
                                          {%
                                          +1%
                                          myparserdef@argcount
                                          }%<<<
                                          mynewdefmyparserdef@argcount@d#1#2%>>>
                                          {%
                                          +1%
                                          myparserdef@argcount
                                          }%<<<
                                          mynewdefmyparserdef@argcount@D#1#2#3%>>>
                                          {%
                                          +1%
                                          myparserdef@argcount
                                          }%<<<
                                          mynewdefmyparserdef@argcount@r#1%>>>
                                          {%
                                          +1%
                                          myparserdef@argcount
                                          }%<<<
                                          mynewdefmyparserdef@argcount@t#1%>>>
                                          {%
                                          +1%
                                          myparserdef@argcount
                                          }%<<<
                                          mynewdefmyparser@name#1%>>>
                                          {%
                                          myparser #1%
                                          }%<<<
                                          mynewdefmyparser@rule#1%>>>
                                          {%
                                          myparser@currentspace #1space meaningmyparser@token
                                          }%<<<
                                          mynewdefmyparser@type#1%>>>
                                          {%
                                          myparser@rule{#1} type%
                                          }%<<<
                                          mynewdefmyparser@code#1%>>>
                                          {%
                                          myparser@rule{#1} code%
                                          }%<<<
                                          mynewdef[protected]myparserrun#1%>>>
                                          {%
                                          myifcsundefTF{myparser@name{#1}}
                                          {PackageError{my}{No parser named '#1' defined}{}}
                                          {%
                                          edefmyparser@current{myparser@name{#1}}%
                                          defmyparser@usersname{#1}%
                                          defmyparser@state{initial}%
                                          myparser@getnexttoken
                                          }%
                                          }%<<<
                                          mynewdef[protected]myparser@getnexttoken%>>>
                                          {%
                                          ifxmyparser@statemyparser@final
                                          myfi@An
                                          else
                                          myfi@By
                                          fi
                                          {%
                                          afterassignmentmyparser@getnexttoken@a
                                          letmyparser@token= % space after = to get spaces, too
                                          }%
                                          }%<<<
                                          mynewdef[protected]myparser@getnexttoken@a%>>>
                                          {%
                                          myifcsundefTF{myparser@type{myparser@state}}
                                          {%
                                          myifcsundefTF{myparser@type{all}}
                                          {%
                                          PackageError{my}
                                          {%
                                          No rule for parser 'myparser@usersname' in state
                                          'myparser@state' for 'meaningmyparser@token'.
                                          Ignoring token%
                                          }
                                          {}%
                                          myparser@getnexttoken
                                          }
                                          {myparser@handle{all}}%
                                          }
                                          {myparser@handle{myparser@state}}%
                                          }%<<<
                                          mynewdef[protected]myparser@handle#1%>>>
                                          {%
                                          expandafterifxcsnamemyparser@type{#1}endcsnamemyparser@noarg
                                          myfi@BTb
                                          fi
                                          @secondoftwo
                                          {csnamemyparser@code{#1}endcsname}
                                          {myparser@handle@args{#1}}%
                                          }%<<<
                                          mynewdef[protected]myparserstate#1%>>>
                                          {%
                                          defmyparser@state{#1}%
                                          }%<<<
                                          mynewdef[protected]myparser@handle@args#1%>>>
                                          {%
                                          defmyparser@stateorall{#1}%
                                          expandafterexpandafterexpandaftermyparser@handle@args@a
                                          csnamemyparser@type{#1}endcsnamemy@markmy@stop
                                          }%<<<
                                          mynewdefmyparser@handle@args@a%>>>
                                          {%
                                          myparser@handle@args@b{}%
                                          }%<<<
                                          mynewdef[long]myparser@handle@args@b#1#2#3my@stop%>>>
                                          {%
                                          my@ifmark{#2}
                                          {csnamemyparser@code{myparser@stateorall}endcsname#1}
                                          {%
                                          myifcsundefTF{myparser@handle@args@#2}
                                          {PackageError{my}{Unknown argument type '#2'}{}}
                                          {csname myparser@handle@args@#2endcsname{#1}{#3}}%
                                          }%
                                          }%<<<
                                          mynewdef[long]myparser@handle@args@c#1#2%>>>
                                          {%
                                          my@ifmark{#2}
                                          {csnamemyparser@code{myparser@stateorall}endcsname#1}
                                          {myparser@handle@args@b{#1}#2my@stop}%
                                          }%<<<
                                          mynewdef[long]myparser@handle@args@m#1#2#3%>>>
                                          {%
                                          myparser@handle@args@c{#1{#3}}{#2}%
                                          }%<<<
                                          mynewdef[protectedlong]myparser@handle@args@o#1#2%>>>
                                          {%
                                          myoarg@oarg{myparser@handle@args@m{#1}{#2}}%
                                          }%<<<
                                          mynewdef[long]myparser@handle@args@O#1#2%>>>
                                          {%
                                          myparser@handle@args@O@{#1}#2my@stop
                                          }%<<<
                                          mynewdef[protectedlong]myparser@handle@args@O@#1#2#3my@stop%>>>
                                          {%
                                          myoarg@Oarg{#2}{myparser@handle@args@m{#1}{#3}}%
                                          }%<<<
                                          mynewdef[long]myparser@handle@args@d#1#2%>>>
                                          {%
                                          myparser@handle@args@d@{#1}#2my@stop
                                          }%<<<
                                          mynewdef[protectedlong]myparser@handle@args@d@#1#2#3#4my@stop%>>>
                                          {%
                                          myoarg@darg{#2}{#3}{myparser@handle@args@m{#1}{#4}}%
                                          }%<<<
                                          mynewdef[long]myparser@handle@args@D#1#2%>>>
                                          {%
                                          myparser@handle@args@D@{#1}#2my@stop
                                          }%<<<
                                          mynewdef[protectedlong]myparser@handle@args@D@#1#2#3#4#5my@stop%>>>
                                          {%
                                          myoarg@Darg{#2}{#3}{#4}{myparser@handle@args@m{#1}{#5}}%
                                          }%<<<
                                          mynewdef[long]myparser@handle@args@r#1#2%>>>
                                          {%
                                          myparser@handle@args@r@a{#1}#2my@stop
                                          }%<<<
                                          mynewdef[protectedlong]myparser@handle@args@r@a#1#2#3my@stop%>>>
                                          {%
                                          defmyparser@handle@args@r@b##1#2{myparser@handle@args@c{#1{##1}}{#3}}%
                                          myparser@handle@args@r@b
                                          }%<<<
                                          mynewdef[long]myparser@handle@args@t#1#2%>>>
                                          {%
                                          myparser@handle@args@t@a{#1}#2my@stop
                                          }%<<<
                                          mynewdef[protectedlong]myparser@handle@args@t@a#1#2#3my@stop%>>>
                                          {%
                                          @ifnextchar#2%
                                          {@firstoftwo{myparser@handle@args@c{#1{my@mark}}{#3}}}
                                          {myparser@handle@args@c{#1{my@stop}}{#3}}%
                                          }%<<<
                                          letmyIfNoValueTFmy@ifmark
                                          letmyIfBooleanTFmy@ifmark
                                          makeatother
                                          % <<<

                                          % the sheet path parser >>>
                                          makeatletter
                                          definsertpath#1{edefsheetpath@{unexpandedexpandafter{sheetpath@#1}}}
                                          defsheetpathcurve#1#2#3#4%
                                          {%
                                          to[out=0,in=180] ++({.5*sheetlength},{#1*sheetheight})
                                          myIfBooleanTF{#3}{}{node[scale=sheetdotsize,inner sep=0pt]{.}}
                                          myIfNoValueTF{#4}{}{coordinate({#4})}
                                          to[out=0,in=180] ++({.5*sheetlength},{#2*sheetheight})
                                          }
                                          defoutputpath{drawsheetpath@;}
                                          defsheet{defsheetpath@{}myparserrun{sheet path}}
                                          makeatother
                                          myparserdef{sheet path}{initial}{the character (}[r,r)]
                                          {insertpath{({#1},{#2*sheetheight})}myparserstate{started}}
                                          myparserdef{sheet path}{initial}{the character =}
                                          {insertpath{(0,0)--++(sheetlength,0)}myparserstate{started}}
                                          myparserdef{sheet path}{started}{the character (}[r)]
                                          {insertpath{coordinate({#1})}}
                                          myparserdef{sheet path}{started}{the character =}
                                          {insertpath{--++(sheetlength,0)}}
                                          myparserdef{sheet path}{started}{the letter u}[txd()]
                                          {insertpath{sheetpathcurve{.5}{-.5}{#1}{#2}}}
                                          myparserdef{sheet path}{started}{the letter U}[txd()]
                                          {insertpath{sheetpathcurve{1}{-1}{#1}{#2}}}
                                          myparserdef{sheet path}{started}{the letter d}[txd()]
                                          {insertpath{sheetpathcurve{-.5}{.5}{#1}{#2}}}
                                          myparserdef{sheet path}{started}{the letter D}[txd()]
                                          {insertpath{sheetpathcurve{-1}{1}{#1}{#2}}}
                                          % making '.' a no-op, that way we can use it to end the search for an optional
                                          % argument for instance
                                          myparserdef{sheet path}{started} .{}
                                          myparserdef{sheet path}{started}{the letter x}[d()]
                                          {%
                                          myIfNoValueTF{#1}
                                          {%
                                          insertpath
                                          {--node[scale=sheetdotsize,inner sep=0pt]{.}++(sheetlength,0)}%
                                          }
                                          {%
                                          insertpath
                                          {%
                                          --node[scale=sheetdotsize,inner sep=0pt]{.}
                                          coordinate({#1})
                                          ++(sheetlength,0)
                                          }%
                                          }%
                                          }
                                          myparserdef{sheet path}{all}{the character ;}{myparserstate{final}outputpath}
                                          % <<<

                                          % sheet height and sheet length >>>
                                          pgfset
                                          {
                                          ,sheet height/.store in=sheetheight
                                          ,sheet height=1
                                          ,sheet length/.store in=sheetlength
                                          ,sheet length=1
                                          ,sheet dot size/.store in=sheetdotsize
                                          ,sheet dot size=4
                                          }
                                          %<<<

                                          begin{document}
                                          begin{tikzpicture}
                                          begin{scope}[thick, sheet height=0.75]
                                          sheet === ===d(sp1)=;
                                          sheet (0,-1) ==d(sp2)===ux =;
                                          sheet (0,-2) ==ux ===Dx =;
                                          sheet (0,-3) === ==== =;
                                          sheet (0,-4) === ===U(sp3)=;
                                          sheet (0,-5.5) ==x(b1) ===x(b2) =;
                                          end{scope}
                                          draw[dashed]
                                          (b2) -- (sp1)
                                          (b1) -- (sp2)
                                          ;
                                          end{tikzpicture}
                                          end{document}


                                          enter image description here






                                          share|improve this answer


























                                          • Wow ! This is a huge work. I'm impressed (like always I'm by the texperts ;)).

                                            – Kpym
                                            7 hours ago














                                          5












                                          5








                                          5







                                          Edit notes:




                                          • spaces can now be handled, but are ignored by default


                                          • alternative syntax for myparserdef added





                                          Inspired by Kpym's answer but thinking that the possibilities of pgfparser are insufficient, I wrote my own parser, that should be similar to pgf's, but allows the parsed elements to grab arguments. The following arguments are supported:





                                          • m a mandatory argument


                                          • r{<delim>} a mandatory argument delimited by <delim>


                                          • o an optional argument in brackets (you can test for it with myIfNoValueTF)


                                          • O{<default>} an optional argument defaulting to <default>


                                          • d<delim1><delim2> an optional argument delimited by <delim1> and <delim2> (you can test for it with myIfNoValueTF)


                                          • D<delim1><delim2>{<default>} an optional argument delimited by <delim1> and <delim2> defaulting to <default>


                                          • t<token> an optional token (you can test for it with myIfBooleanTF)


                                          Despite the fact that the argument names are inspired by xparse, none of them care for balanced delimiters (e.g., [[ab]] would not be grabbed as [ab], but as [ab with an orphaned ], so you'd have to use [{[ab]}], this is like the LaTeX2e behaviour). Also all arguments are long by nature unlike xparse where you'd need to specify that using +.



                                          You can define a parser using myparserdef{<name>}{<state>}{<meaning>}[<args>]{<code>}, with <name> the name of the parser, <state> the state, <meaning> the meaning of a token, <args> an argument string (built from the arguments listed above, up to 9 arguments are supported) and <code> the code which should be executed for that combination of <name>, <state> and <meaning>. You can switch states using myparserstate{<state>}, if you switch to final parsing is ended, the initial state is initial. All in all this is pretty similar to pgfparsers way of doing things. The biggest difference is, that my parser ignores blanks by default, however you can define an action for blanks with myparserdef{<name>}{<state>}{blank space}[<args>]{<code>}. Many consecutive blanks are considered as one.



                                          You can also use a different syntax for myparserdef namely: myparserdef{<name>}{<state>}<token>[<args>]{<code>} with <token> being a single token not surrounded by {} (spaces are ignored here, it is not checked whether <token> is really a single token, so be careful). In that case the same will be done as if you'd typed the meaning of the <token>, so myparserdef{foo}{bar}a{baz} does the same as myparserdef{foo}{bar}{the letter a}{baz}.



                                          A parser is executed using myparserrun{<name>}. A parser needs at least one rule, else an error is thrown.



                                          This parser system allows me to place coordinates inside of sheet, which was the main reason why I found pgfparser insufficient.



                                          I did all of this without using any packages, only LaTeX-Kernel macros, just for procrastinating reasons. Using for example xparse would shorten the code considerably.



                                          documentclass[tikz,border=7pt]{standalone}

                                          % my parser >>>
                                          makeatletter
                                          % logic helpers >>>
                                          longdefmyfi@An#1fi#2{fi}
                                          longdefmyfi@Ay#1fi#2{fi#2}
                                          longdefmyfi@Byfi#1{fi#1}
                                          longdefmyfi@BTbfi#1#2#3{fi#2}
                                          % <<<
                                          % mynewdef >>>
                                          @ifdefinablemyifundefTF%>>>
                                          {%
                                          defmyifundefTF#1%
                                          {%
                                          ifdefined#1%
                                          myfi@Ay
                                          else
                                          myfi@BTb
                                          fi
                                          {%
                                          ifx#1relax
                                          myfi@BTb
                                          fi
                                          @secondoftwo
                                          }%
                                          }%
                                          }%<<<
                                          @ifdefinablemynewdef%>>>
                                          {%
                                          protecteddefmynewdef{@ifnextchar[{mynewdef@a}{mynewdef@a}}%
                                          }%<<<
                                          @ifdefinablemynewdef@a%>>>
                                          {%
                                          longdefmynewdef@a[#1]#2#3#{mynewdef@b{#1}#2{#3}}%
                                          }%<<<
                                          @ifdefinablemynewdef@b%>>>
                                          {%
                                          protectedlongdefmynewdef@b#1#2#3#4%
                                          {%
                                          myifundefTF#2%
                                          {%
                                          #1def#2#3{#4}%
                                          }
                                          {%
                                          PackageError{my}{Command string#2space already defined}{}%
                                          }
                                          }%
                                          }%<<<
                                          mynewdefmyifcsundefTF#1%>>>
                                          {%
                                          ifcsname #1endcsname
                                          myfi@Ay
                                          else
                                          myfi@BTb
                                          fi
                                          {%
                                          expandafterifxcsname #1endcsnamerelax
                                          myfi@BTb
                                          fi
                                          @secondoftwo
                                          }%
                                          }%<<<
                                          % <<<
                                          % opt arg parsing >>>
                                          mynewdef[long]my@ifmark#1%>>>
                                          {%
                                          ifxmy@mark#1%
                                          myfi@BTb
                                          fi
                                          @secondoftwo
                                          }%<<<
                                          mynewdef[protectedlong]myoarg@oarg#1%>>>
                                          {%
                                          @ifnextchar[{myoarg@oarg@{#1}}{#1{my@mark}}%
                                          }%<<<
                                          mynewdef[long]myoarg@oarg@#1[#2]%>>>
                                          {%
                                          #1{#2}%
                                          }%<<<
                                          mynewdef[protectedlong]myoarg@Oarg#1#2%>>>
                                          {%
                                          @ifnextchar[{myoarg@oarg@{#2}}{#2{#1}}%
                                          }%<<<
                                          mynewdef[protectedlong]myoarg@darg#1#2#3%>>>
                                          {%
                                          longdefmyoarg@darg@##1#1##2#2{##1{##2}}%
                                          @ifnextchar#1{myoarg@darg@{#3}}{#3{my@mark}}%
                                          }%<<<
                                          mynewdef[protectedlong]myoarg@Darg#1#2#3#4%>>>
                                          {%
                                          longdefmyoarg@darg@##1#1##2#2{##1{##2}}%
                                          @ifnextchar#1{myoarg@darg@{#4}}{#4{#3}}%
                                          }%<<<
                                          % <<<
                                          % macros for string comparison >>>
                                          begingroupdef:{endgroupletmy@sptoken= }:
                                          mynewdefmy@mark{my@mark@if@you@see@this@report@it}
                                          mynewdefmy@stop{my@stop@if@you@see@this@report@it}
                                          mynewdefmyparser@final{final}
                                          mynewdefmyparser@noarg{noarg}
                                          mynewdefmyparser@blankspace{blank space}
                                          % <<<
                                          mynewdef[protected]myparserdef#1#2%>>>
                                          {%
                                          defmyparserdef@twoargs{{#1}{#2}}%
                                          myparserdef@a
                                          }%<<<
                                          mynewdef[protected]myparserdef@a%>>>
                                          {%
                                          futureletmyparserdef@argmyparserdef@b
                                          }%<<<
                                          mynewdefmyparserdef@b%>>>
                                          {%
                                          ifxmyparserdef@argmy@sptoken
                                          myfi@BTb
                                          fi
                                          @secondoftwo
                                          {myparserdef@gobble@space}
                                          {myparserdef@c}%
                                          }%<<<
                                          mynewdef[protected]myparserdef@gobble@space%>>>
                                          {%
                                          afterassignmentmyparserdef@a
                                          letmyparserdef@arg= % space after = to get spaces, too
                                          }%<<<
                                          mynewdef[protected]myparserdef@c#1%>>>
                                          {%
                                          ifxmyparserdef@argbgroup
                                          myfi@BTb
                                          fi
                                          @secondoftwo
                                          {%
                                          defmyparserdef@arg{#1}%
                                          ifxmyparser@blankspacemyparserdef@arg
                                          myfi@BTb
                                          fi
                                          @secondoftwo
                                          {expandaftermyparserdef@dmyparserdef@twoargs{blank space space}}
                                          {expandaftermyparserdef@dmyparserdef@twoargs{#1}}%
                                          }
                                          {expandaftermyparserdef@dmyparserdef@twoargs{meaningmyparserdef@arg}}%
                                          }%<<<
                                          mynewdef[long]myparserdef@d#1#2#3%>>>
                                          {%
                                          myoarg@oarg{myparserdef@e{#1}{#2}{#3}}%
                                          }%<<<
                                          mynewdef[protectedlong]myparserdef@e#1#2#3#4#5%>>>
                                          {%
                                          % if that is the first rule for the parser, define space to be a no-op
                                          myifcsundefTF{myparser@name{#1}}%
                                          {%
                                          expandafterdef
                                          csname myparser@name{#1} all blank space spacespace typeendcsname
                                          {noarg}%
                                          expandafterdef
                                          csname myparser@name{#1} all blank space spacespace codeendcsname
                                          {myparser@getnexttoken}%
                                          % use a macro as a flag that there is at least one parser rule defined
                                          expandafterdefcsnamemyparser@name{#1}endcsname{}%
                                          }
                                          {}%
                                          % check whether the optional argument was used
                                          my@ifmark{#4}
                                          {%
                                          % use a macro as flag that there is a rule for the specified state
                                          expandafterdefcsname myparser@name{#1} #2 #3 typeendcsname{noarg}%
                                          defmyparserdef@arg@count{0}%
                                          }
                                          {%
                                          edefmyparserdef@arg@count
                                          {thenumexprmyparserdef@argcount#4my@mark}%
                                          ifnummyparserdef@arg@count>9%
                                          PackageError{my}{Too many arguments for parser rule}
                                          {A maximum of 9 parameters is supported.}%
                                          else
                                          ifnummyparserdef@arg@count=0%
                                          expandafterdefcsname myparser@name{#1} #2 #3 typeendcsname
                                          {noarg}%
                                          else
                                          expandafterdefcsname myparser@name{#1} #2 #3 typeendcsname{#4}%
                                          fi
                                          fi
                                          }%
                                          % define what the code does
                                          expandafterdefcsname myparser@name{#1} #2 #3 codeendcsname{}%
                                          expandafterrenewcommandcsname myparser@name{#1} #2 #3 codeendcsname
                                          [myparserdef@arg@count]{#5myparser@getnexttoken}%
                                          }%<<<
                                          mynewdefmyparserdef@argcount#1%>>>
                                          {%
                                          ifxmy@mark#1%
                                          myfi@An
                                          else
                                          myfi@By
                                          fi
                                          {csname myparserdef@argcount@#1endcsname}%
                                          }%<<<
                                          mynewdefmyparserdef@argcount@m%>>>
                                          {%
                                          +1%
                                          myparserdef@argcount
                                          }%<<<
                                          mynewdefmyparserdef@argcount@o%>>>
                                          {%
                                          +1%
                                          myparserdef@argcount
                                          }%<<<
                                          mynewdefmyparserdef@argcount@O#1%>>>
                                          {%
                                          +1%
                                          myparserdef@argcount
                                          }%<<<
                                          mynewdefmyparserdef@argcount@d#1#2%>>>
                                          {%
                                          +1%
                                          myparserdef@argcount
                                          }%<<<
                                          mynewdefmyparserdef@argcount@D#1#2#3%>>>
                                          {%
                                          +1%
                                          myparserdef@argcount
                                          }%<<<
                                          mynewdefmyparserdef@argcount@r#1%>>>
                                          {%
                                          +1%
                                          myparserdef@argcount
                                          }%<<<
                                          mynewdefmyparserdef@argcount@t#1%>>>
                                          {%
                                          +1%
                                          myparserdef@argcount
                                          }%<<<
                                          mynewdefmyparser@name#1%>>>
                                          {%
                                          myparser #1%
                                          }%<<<
                                          mynewdefmyparser@rule#1%>>>
                                          {%
                                          myparser@currentspace #1space meaningmyparser@token
                                          }%<<<
                                          mynewdefmyparser@type#1%>>>
                                          {%
                                          myparser@rule{#1} type%
                                          }%<<<
                                          mynewdefmyparser@code#1%>>>
                                          {%
                                          myparser@rule{#1} code%
                                          }%<<<
                                          mynewdef[protected]myparserrun#1%>>>
                                          {%
                                          myifcsundefTF{myparser@name{#1}}
                                          {PackageError{my}{No parser named '#1' defined}{}}
                                          {%
                                          edefmyparser@current{myparser@name{#1}}%
                                          defmyparser@usersname{#1}%
                                          defmyparser@state{initial}%
                                          myparser@getnexttoken
                                          }%
                                          }%<<<
                                          mynewdef[protected]myparser@getnexttoken%>>>
                                          {%
                                          ifxmyparser@statemyparser@final
                                          myfi@An
                                          else
                                          myfi@By
                                          fi
                                          {%
                                          afterassignmentmyparser@getnexttoken@a
                                          letmyparser@token= % space after = to get spaces, too
                                          }%
                                          }%<<<
                                          mynewdef[protected]myparser@getnexttoken@a%>>>
                                          {%
                                          myifcsundefTF{myparser@type{myparser@state}}
                                          {%
                                          myifcsundefTF{myparser@type{all}}
                                          {%
                                          PackageError{my}
                                          {%
                                          No rule for parser 'myparser@usersname' in state
                                          'myparser@state' for 'meaningmyparser@token'.
                                          Ignoring token%
                                          }
                                          {}%
                                          myparser@getnexttoken
                                          }
                                          {myparser@handle{all}}%
                                          }
                                          {myparser@handle{myparser@state}}%
                                          }%<<<
                                          mynewdef[protected]myparser@handle#1%>>>
                                          {%
                                          expandafterifxcsnamemyparser@type{#1}endcsnamemyparser@noarg
                                          myfi@BTb
                                          fi
                                          @secondoftwo
                                          {csnamemyparser@code{#1}endcsname}
                                          {myparser@handle@args{#1}}%
                                          }%<<<
                                          mynewdef[protected]myparserstate#1%>>>
                                          {%
                                          defmyparser@state{#1}%
                                          }%<<<
                                          mynewdef[protected]myparser@handle@args#1%>>>
                                          {%
                                          defmyparser@stateorall{#1}%
                                          expandafterexpandafterexpandaftermyparser@handle@args@a
                                          csnamemyparser@type{#1}endcsnamemy@markmy@stop
                                          }%<<<
                                          mynewdefmyparser@handle@args@a%>>>
                                          {%
                                          myparser@handle@args@b{}%
                                          }%<<<
                                          mynewdef[long]myparser@handle@args@b#1#2#3my@stop%>>>
                                          {%
                                          my@ifmark{#2}
                                          {csnamemyparser@code{myparser@stateorall}endcsname#1}
                                          {%
                                          myifcsundefTF{myparser@handle@args@#2}
                                          {PackageError{my}{Unknown argument type '#2'}{}}
                                          {csname myparser@handle@args@#2endcsname{#1}{#3}}%
                                          }%
                                          }%<<<
                                          mynewdef[long]myparser@handle@args@c#1#2%>>>
                                          {%
                                          my@ifmark{#2}
                                          {csnamemyparser@code{myparser@stateorall}endcsname#1}
                                          {myparser@handle@args@b{#1}#2my@stop}%
                                          }%<<<
                                          mynewdef[long]myparser@handle@args@m#1#2#3%>>>
                                          {%
                                          myparser@handle@args@c{#1{#3}}{#2}%
                                          }%<<<
                                          mynewdef[protectedlong]myparser@handle@args@o#1#2%>>>
                                          {%
                                          myoarg@oarg{myparser@handle@args@m{#1}{#2}}%
                                          }%<<<
                                          mynewdef[long]myparser@handle@args@O#1#2%>>>
                                          {%
                                          myparser@handle@args@O@{#1}#2my@stop
                                          }%<<<
                                          mynewdef[protectedlong]myparser@handle@args@O@#1#2#3my@stop%>>>
                                          {%
                                          myoarg@Oarg{#2}{myparser@handle@args@m{#1}{#3}}%
                                          }%<<<
                                          mynewdef[long]myparser@handle@args@d#1#2%>>>
                                          {%
                                          myparser@handle@args@d@{#1}#2my@stop
                                          }%<<<
                                          mynewdef[protectedlong]myparser@handle@args@d@#1#2#3#4my@stop%>>>
                                          {%
                                          myoarg@darg{#2}{#3}{myparser@handle@args@m{#1}{#4}}%
                                          }%<<<
                                          mynewdef[long]myparser@handle@args@D#1#2%>>>
                                          {%
                                          myparser@handle@args@D@{#1}#2my@stop
                                          }%<<<
                                          mynewdef[protectedlong]myparser@handle@args@D@#1#2#3#4#5my@stop%>>>
                                          {%
                                          myoarg@Darg{#2}{#3}{#4}{myparser@handle@args@m{#1}{#5}}%
                                          }%<<<
                                          mynewdef[long]myparser@handle@args@r#1#2%>>>
                                          {%
                                          myparser@handle@args@r@a{#1}#2my@stop
                                          }%<<<
                                          mynewdef[protectedlong]myparser@handle@args@r@a#1#2#3my@stop%>>>
                                          {%
                                          defmyparser@handle@args@r@b##1#2{myparser@handle@args@c{#1{##1}}{#3}}%
                                          myparser@handle@args@r@b
                                          }%<<<
                                          mynewdef[long]myparser@handle@args@t#1#2%>>>
                                          {%
                                          myparser@handle@args@t@a{#1}#2my@stop
                                          }%<<<
                                          mynewdef[protectedlong]myparser@handle@args@t@a#1#2#3my@stop%>>>
                                          {%
                                          @ifnextchar#2%
                                          {@firstoftwo{myparser@handle@args@c{#1{my@mark}}{#3}}}
                                          {myparser@handle@args@c{#1{my@stop}}{#3}}%
                                          }%<<<
                                          letmyIfNoValueTFmy@ifmark
                                          letmyIfBooleanTFmy@ifmark
                                          makeatother
                                          % <<<

                                          % the sheet path parser >>>
                                          makeatletter
                                          definsertpath#1{edefsheetpath@{unexpandedexpandafter{sheetpath@#1}}}
                                          defsheetpathcurve#1#2#3#4%
                                          {%
                                          to[out=0,in=180] ++({.5*sheetlength},{#1*sheetheight})
                                          myIfBooleanTF{#3}{}{node[scale=sheetdotsize,inner sep=0pt]{.}}
                                          myIfNoValueTF{#4}{}{coordinate({#4})}
                                          to[out=0,in=180] ++({.5*sheetlength},{#2*sheetheight})
                                          }
                                          defoutputpath{drawsheetpath@;}
                                          defsheet{defsheetpath@{}myparserrun{sheet path}}
                                          makeatother
                                          myparserdef{sheet path}{initial}{the character (}[r,r)]
                                          {insertpath{({#1},{#2*sheetheight})}myparserstate{started}}
                                          myparserdef{sheet path}{initial}{the character =}
                                          {insertpath{(0,0)--++(sheetlength,0)}myparserstate{started}}
                                          myparserdef{sheet path}{started}{the character (}[r)]
                                          {insertpath{coordinate({#1})}}
                                          myparserdef{sheet path}{started}{the character =}
                                          {insertpath{--++(sheetlength,0)}}
                                          myparserdef{sheet path}{started}{the letter u}[txd()]
                                          {insertpath{sheetpathcurve{.5}{-.5}{#1}{#2}}}
                                          myparserdef{sheet path}{started}{the letter U}[txd()]
                                          {insertpath{sheetpathcurve{1}{-1}{#1}{#2}}}
                                          myparserdef{sheet path}{started}{the letter d}[txd()]
                                          {insertpath{sheetpathcurve{-.5}{.5}{#1}{#2}}}
                                          myparserdef{sheet path}{started}{the letter D}[txd()]
                                          {insertpath{sheetpathcurve{-1}{1}{#1}{#2}}}
                                          % making '.' a no-op, that way we can use it to end the search for an optional
                                          % argument for instance
                                          myparserdef{sheet path}{started} .{}
                                          myparserdef{sheet path}{started}{the letter x}[d()]
                                          {%
                                          myIfNoValueTF{#1}
                                          {%
                                          insertpath
                                          {--node[scale=sheetdotsize,inner sep=0pt]{.}++(sheetlength,0)}%
                                          }
                                          {%
                                          insertpath
                                          {%
                                          --node[scale=sheetdotsize,inner sep=0pt]{.}
                                          coordinate({#1})
                                          ++(sheetlength,0)
                                          }%
                                          }%
                                          }
                                          myparserdef{sheet path}{all}{the character ;}{myparserstate{final}outputpath}
                                          % <<<

                                          % sheet height and sheet length >>>
                                          pgfset
                                          {
                                          ,sheet height/.store in=sheetheight
                                          ,sheet height=1
                                          ,sheet length/.store in=sheetlength
                                          ,sheet length=1
                                          ,sheet dot size/.store in=sheetdotsize
                                          ,sheet dot size=4
                                          }
                                          %<<<

                                          begin{document}
                                          begin{tikzpicture}
                                          begin{scope}[thick, sheet height=0.75]
                                          sheet === ===d(sp1)=;
                                          sheet (0,-1) ==d(sp2)===ux =;
                                          sheet (0,-2) ==ux ===Dx =;
                                          sheet (0,-3) === ==== =;
                                          sheet (0,-4) === ===U(sp3)=;
                                          sheet (0,-5.5) ==x(b1) ===x(b2) =;
                                          end{scope}
                                          draw[dashed]
                                          (b2) -- (sp1)
                                          (b1) -- (sp2)
                                          ;
                                          end{tikzpicture}
                                          end{document}


                                          enter image description here






                                          share|improve this answer















                                          Edit notes:




                                          • spaces can now be handled, but are ignored by default


                                          • alternative syntax for myparserdef added





                                          Inspired by Kpym's answer but thinking that the possibilities of pgfparser are insufficient, I wrote my own parser, that should be similar to pgf's, but allows the parsed elements to grab arguments. The following arguments are supported:





                                          • m a mandatory argument


                                          • r{<delim>} a mandatory argument delimited by <delim>


                                          • o an optional argument in brackets (you can test for it with myIfNoValueTF)


                                          • O{<default>} an optional argument defaulting to <default>


                                          • d<delim1><delim2> an optional argument delimited by <delim1> and <delim2> (you can test for it with myIfNoValueTF)


                                          • D<delim1><delim2>{<default>} an optional argument delimited by <delim1> and <delim2> defaulting to <default>


                                          • t<token> an optional token (you can test for it with myIfBooleanTF)


                                          Despite the fact that the argument names are inspired by xparse, none of them care for balanced delimiters (e.g., [[ab]] would not be grabbed as [ab], but as [ab with an orphaned ], so you'd have to use [{[ab]}], this is like the LaTeX2e behaviour). Also all arguments are long by nature unlike xparse where you'd need to specify that using +.



                                          You can define a parser using myparserdef{<name>}{<state>}{<meaning>}[<args>]{<code>}, with <name> the name of the parser, <state> the state, <meaning> the meaning of a token, <args> an argument string (built from the arguments listed above, up to 9 arguments are supported) and <code> the code which should be executed for that combination of <name>, <state> and <meaning>. You can switch states using myparserstate{<state>}, if you switch to final parsing is ended, the initial state is initial. All in all this is pretty similar to pgfparsers way of doing things. The biggest difference is, that my parser ignores blanks by default, however you can define an action for blanks with myparserdef{<name>}{<state>}{blank space}[<args>]{<code>}. Many consecutive blanks are considered as one.



                                          You can also use a different syntax for myparserdef namely: myparserdef{<name>}{<state>}<token>[<args>]{<code>} with <token> being a single token not surrounded by {} (spaces are ignored here, it is not checked whether <token> is really a single token, so be careful). In that case the same will be done as if you'd typed the meaning of the <token>, so myparserdef{foo}{bar}a{baz} does the same as myparserdef{foo}{bar}{the letter a}{baz}.



                                          A parser is executed using myparserrun{<name>}. A parser needs at least one rule, else an error is thrown.



                                          This parser system allows me to place coordinates inside of sheet, which was the main reason why I found pgfparser insufficient.



                                          I did all of this without using any packages, only LaTeX-Kernel macros, just for procrastinating reasons. Using for example xparse would shorten the code considerably.



                                          documentclass[tikz,border=7pt]{standalone}

                                          % my parser >>>
                                          makeatletter
                                          % logic helpers >>>
                                          longdefmyfi@An#1fi#2{fi}
                                          longdefmyfi@Ay#1fi#2{fi#2}
                                          longdefmyfi@Byfi#1{fi#1}
                                          longdefmyfi@BTbfi#1#2#3{fi#2}
                                          % <<<
                                          % mynewdef >>>
                                          @ifdefinablemyifundefTF%>>>
                                          {%
                                          defmyifundefTF#1%
                                          {%
                                          ifdefined#1%
                                          myfi@Ay
                                          else
                                          myfi@BTb
                                          fi
                                          {%
                                          ifx#1relax
                                          myfi@BTb
                                          fi
                                          @secondoftwo
                                          }%
                                          }%
                                          }%<<<
                                          @ifdefinablemynewdef%>>>
                                          {%
                                          protecteddefmynewdef{@ifnextchar[{mynewdef@a}{mynewdef@a}}%
                                          }%<<<
                                          @ifdefinablemynewdef@a%>>>
                                          {%
                                          longdefmynewdef@a[#1]#2#3#{mynewdef@b{#1}#2{#3}}%
                                          }%<<<
                                          @ifdefinablemynewdef@b%>>>
                                          {%
                                          protectedlongdefmynewdef@b#1#2#3#4%
                                          {%
                                          myifundefTF#2%
                                          {%
                                          #1def#2#3{#4}%
                                          }
                                          {%
                                          PackageError{my}{Command string#2space already defined}{}%
                                          }
                                          }%
                                          }%<<<
                                          mynewdefmyifcsundefTF#1%>>>
                                          {%
                                          ifcsname #1endcsname
                                          myfi@Ay
                                          else
                                          myfi@BTb
                                          fi
                                          {%
                                          expandafterifxcsname #1endcsnamerelax
                                          myfi@BTb
                                          fi
                                          @secondoftwo
                                          }%
                                          }%<<<
                                          % <<<
                                          % opt arg parsing >>>
                                          mynewdef[long]my@ifmark#1%>>>
                                          {%
                                          ifxmy@mark#1%
                                          myfi@BTb
                                          fi
                                          @secondoftwo
                                          }%<<<
                                          mynewdef[protectedlong]myoarg@oarg#1%>>>
                                          {%
                                          @ifnextchar[{myoarg@oarg@{#1}}{#1{my@mark}}%
                                          }%<<<
                                          mynewdef[long]myoarg@oarg@#1[#2]%>>>
                                          {%
                                          #1{#2}%
                                          }%<<<
                                          mynewdef[protectedlong]myoarg@Oarg#1#2%>>>
                                          {%
                                          @ifnextchar[{myoarg@oarg@{#2}}{#2{#1}}%
                                          }%<<<
                                          mynewdef[protectedlong]myoarg@darg#1#2#3%>>>
                                          {%
                                          longdefmyoarg@darg@##1#1##2#2{##1{##2}}%
                                          @ifnextchar#1{myoarg@darg@{#3}}{#3{my@mark}}%
                                          }%<<<
                                          mynewdef[protectedlong]myoarg@Darg#1#2#3#4%>>>
                                          {%
                                          longdefmyoarg@darg@##1#1##2#2{##1{##2}}%
                                          @ifnextchar#1{myoarg@darg@{#4}}{#4{#3}}%
                                          }%<<<
                                          % <<<
                                          % macros for string comparison >>>
                                          begingroupdef:{endgroupletmy@sptoken= }:
                                          mynewdefmy@mark{my@mark@if@you@see@this@report@it}
                                          mynewdefmy@stop{my@stop@if@you@see@this@report@it}
                                          mynewdefmyparser@final{final}
                                          mynewdefmyparser@noarg{noarg}
                                          mynewdefmyparser@blankspace{blank space}
                                          % <<<
                                          mynewdef[protected]myparserdef#1#2%>>>
                                          {%
                                          defmyparserdef@twoargs{{#1}{#2}}%
                                          myparserdef@a
                                          }%<<<
                                          mynewdef[protected]myparserdef@a%>>>
                                          {%
                                          futureletmyparserdef@argmyparserdef@b
                                          }%<<<
                                          mynewdefmyparserdef@b%>>>
                                          {%
                                          ifxmyparserdef@argmy@sptoken
                                          myfi@BTb
                                          fi
                                          @secondoftwo
                                          {myparserdef@gobble@space}
                                          {myparserdef@c}%
                                          }%<<<
                                          mynewdef[protected]myparserdef@gobble@space%>>>
                                          {%
                                          afterassignmentmyparserdef@a
                                          letmyparserdef@arg= % space after = to get spaces, too
                                          }%<<<
                                          mynewdef[protected]myparserdef@c#1%>>>
                                          {%
                                          ifxmyparserdef@argbgroup
                                          myfi@BTb
                                          fi
                                          @secondoftwo
                                          {%
                                          defmyparserdef@arg{#1}%
                                          ifxmyparser@blankspacemyparserdef@arg
                                          myfi@BTb
                                          fi
                                          @secondoftwo
                                          {expandaftermyparserdef@dmyparserdef@twoargs{blank space space}}
                                          {expandaftermyparserdef@dmyparserdef@twoargs{#1}}%
                                          }
                                          {expandaftermyparserdef@dmyparserdef@twoargs{meaningmyparserdef@arg}}%
                                          }%<<<
                                          mynewdef[long]myparserdef@d#1#2#3%>>>
                                          {%
                                          myoarg@oarg{myparserdef@e{#1}{#2}{#3}}%
                                          }%<<<
                                          mynewdef[protectedlong]myparserdef@e#1#2#3#4#5%>>>
                                          {%
                                          % if that is the first rule for the parser, define space to be a no-op
                                          myifcsundefTF{myparser@name{#1}}%
                                          {%
                                          expandafterdef
                                          csname myparser@name{#1} all blank space spacespace typeendcsname
                                          {noarg}%
                                          expandafterdef
                                          csname myparser@name{#1} all blank space spacespace codeendcsname
                                          {myparser@getnexttoken}%
                                          % use a macro as a flag that there is at least one parser rule defined
                                          expandafterdefcsnamemyparser@name{#1}endcsname{}%
                                          }
                                          {}%
                                          % check whether the optional argument was used
                                          my@ifmark{#4}
                                          {%
                                          % use a macro as flag that there is a rule for the specified state
                                          expandafterdefcsname myparser@name{#1} #2 #3 typeendcsname{noarg}%
                                          defmyparserdef@arg@count{0}%
                                          }
                                          {%
                                          edefmyparserdef@arg@count
                                          {thenumexprmyparserdef@argcount#4my@mark}%
                                          ifnummyparserdef@arg@count>9%
                                          PackageError{my}{Too many arguments for parser rule}
                                          {A maximum of 9 parameters is supported.}%
                                          else
                                          ifnummyparserdef@arg@count=0%
                                          expandafterdefcsname myparser@name{#1} #2 #3 typeendcsname
                                          {noarg}%
                                          else
                                          expandafterdefcsname myparser@name{#1} #2 #3 typeendcsname{#4}%
                                          fi
                                          fi
                                          }%
                                          % define what the code does
                                          expandafterdefcsname myparser@name{#1} #2 #3 codeendcsname{}%
                                          expandafterrenewcommandcsname myparser@name{#1} #2 #3 codeendcsname
                                          [myparserdef@arg@count]{#5myparser@getnexttoken}%
                                          }%<<<
                                          mynewdefmyparserdef@argcount#1%>>>
                                          {%
                                          ifxmy@mark#1%
                                          myfi@An
                                          else
                                          myfi@By
                                          fi
                                          {csname myparserdef@argcount@#1endcsname}%
                                          }%<<<
                                          mynewdefmyparserdef@argcount@m%>>>
                                          {%
                                          +1%
                                          myparserdef@argcount
                                          }%<<<
                                          mynewdefmyparserdef@argcount@o%>>>
                                          {%
                                          +1%
                                          myparserdef@argcount
                                          }%<<<
                                          mynewdefmyparserdef@argcount@O#1%>>>
                                          {%
                                          +1%
                                          myparserdef@argcount
                                          }%<<<
                                          mynewdefmyparserdef@argcount@d#1#2%>>>
                                          {%
                                          +1%
                                          myparserdef@argcount
                                          }%<<<
                                          mynewdefmyparserdef@argcount@D#1#2#3%>>>
                                          {%
                                          +1%
                                          myparserdef@argcount
                                          }%<<<
                                          mynewdefmyparserdef@argcount@r#1%>>>
                                          {%
                                          +1%
                                          myparserdef@argcount
                                          }%<<<
                                          mynewdefmyparserdef@argcount@t#1%>>>
                                          {%
                                          +1%
                                          myparserdef@argcount
                                          }%<<<
                                          mynewdefmyparser@name#1%>>>
                                          {%
                                          myparser #1%
                                          }%<<<
                                          mynewdefmyparser@rule#1%>>>
                                          {%
                                          myparser@currentspace #1space meaningmyparser@token
                                          }%<<<
                                          mynewdefmyparser@type#1%>>>
                                          {%
                                          myparser@rule{#1} type%
                                          }%<<<
                                          mynewdefmyparser@code#1%>>>
                                          {%
                                          myparser@rule{#1} code%
                                          }%<<<
                                          mynewdef[protected]myparserrun#1%>>>
                                          {%
                                          myifcsundefTF{myparser@name{#1}}
                                          {PackageError{my}{No parser named '#1' defined}{}}
                                          {%
                                          edefmyparser@current{myparser@name{#1}}%
                                          defmyparser@usersname{#1}%
                                          defmyparser@state{initial}%
                                          myparser@getnexttoken
                                          }%
                                          }%<<<
                                          mynewdef[protected]myparser@getnexttoken%>>>
                                          {%
                                          ifxmyparser@statemyparser@final
                                          myfi@An
                                          else
                                          myfi@By
                                          fi
                                          {%
                                          afterassignmentmyparser@getnexttoken@a
                                          letmyparser@token= % space after = to get spaces, too
                                          }%
                                          }%<<<
                                          mynewdef[protected]myparser@getnexttoken@a%>>>
                                          {%
                                          myifcsundefTF{myparser@type{myparser@state}}
                                          {%
                                          myifcsundefTF{myparser@type{all}}
                                          {%
                                          PackageError{my}
                                          {%
                                          No rule for parser 'myparser@usersname' in state
                                          'myparser@state' for 'meaningmyparser@token'.
                                          Ignoring token%
                                          }
                                          {}%
                                          myparser@getnexttoken
                                          }
                                          {myparser@handle{all}}%
                                          }
                                          {myparser@handle{myparser@state}}%
                                          }%<<<
                                          mynewdef[protected]myparser@handle#1%>>>
                                          {%
                                          expandafterifxcsnamemyparser@type{#1}endcsnamemyparser@noarg
                                          myfi@BTb
                                          fi
                                          @secondoftwo
                                          {csnamemyparser@code{#1}endcsname}
                                          {myparser@handle@args{#1}}%
                                          }%<<<
                                          mynewdef[protected]myparserstate#1%>>>
                                          {%
                                          defmyparser@state{#1}%
                                          }%<<<
                                          mynewdef[protected]myparser@handle@args#1%>>>
                                          {%
                                          defmyparser@stateorall{#1}%
                                          expandafterexpandafterexpandaftermyparser@handle@args@a
                                          csnamemyparser@type{#1}endcsnamemy@markmy@stop
                                          }%<<<
                                          mynewdefmyparser@handle@args@a%>>>
                                          {%
                                          myparser@handle@args@b{}%
                                          }%<<<
                                          mynewdef[long]myparser@handle@args@b#1#2#3my@stop%>>>
                                          {%
                                          my@ifmark{#2}
                                          {csnamemyparser@code{myparser@stateorall}endcsname#1}
                                          {%
                                          myifcsundefTF{myparser@handle@args@#2}
                                          {PackageError{my}{Unknown argument type '#2'}{}}
                                          {csname myparser@handle@args@#2endcsname{#1}{#3}}%
                                          }%
                                          }%<<<
                                          mynewdef[long]myparser@handle@args@c#1#2%>>>
                                          {%
                                          my@ifmark{#2}
                                          {csnamemyparser@code{myparser@stateorall}endcsname#1}
                                          {myparser@handle@args@b{#1}#2my@stop}%
                                          }%<<<
                                          mynewdef[long]myparser@handle@args@m#1#2#3%>>>
                                          {%
                                          myparser@handle@args@c{#1{#3}}{#2}%
                                          }%<<<
                                          mynewdef[protectedlong]myparser@handle@args@o#1#2%>>>
                                          {%
                                          myoarg@oarg{myparser@handle@args@m{#1}{#2}}%
                                          }%<<<
                                          mynewdef[long]myparser@handle@args@O#1#2%>>>
                                          {%
                                          myparser@handle@args@O@{#1}#2my@stop
                                          }%<<<
                                          mynewdef[protectedlong]myparser@handle@args@O@#1#2#3my@stop%>>>
                                          {%
                                          myoarg@Oarg{#2}{myparser@handle@args@m{#1}{#3}}%
                                          }%<<<
                                          mynewdef[long]myparser@handle@args@d#1#2%>>>
                                          {%
                                          myparser@handle@args@d@{#1}#2my@stop
                                          }%<<<
                                          mynewdef[protectedlong]myparser@handle@args@d@#1#2#3#4my@stop%>>>
                                          {%
                                          myoarg@darg{#2}{#3}{myparser@handle@args@m{#1}{#4}}%
                                          }%<<<
                                          mynewdef[long]myparser@handle@args@D#1#2%>>>
                                          {%
                                          myparser@handle@args@D@{#1}#2my@stop
                                          }%<<<
                                          mynewdef[protectedlong]myparser@handle@args@D@#1#2#3#4#5my@stop%>>>
                                          {%
                                          myoarg@Darg{#2}{#3}{#4}{myparser@handle@args@m{#1}{#5}}%
                                          }%<<<
                                          mynewdef[long]myparser@handle@args@r#1#2%>>>
                                          {%
                                          myparser@handle@args@r@a{#1}#2my@stop
                                          }%<<<
                                          mynewdef[protectedlong]myparser@handle@args@r@a#1#2#3my@stop%>>>
                                          {%
                                          defmyparser@handle@args@r@b##1#2{myparser@handle@args@c{#1{##1}}{#3}}%
                                          myparser@handle@args@r@b
                                          }%<<<
                                          mynewdef[long]myparser@handle@args@t#1#2%>>>
                                          {%
                                          myparser@handle@args@t@a{#1}#2my@stop
                                          }%<<<
                                          mynewdef[protectedlong]myparser@handle@args@t@a#1#2#3my@stop%>>>
                                          {%
                                          @ifnextchar#2%
                                          {@firstoftwo{myparser@handle@args@c{#1{my@mark}}{#3}}}
                                          {myparser@handle@args@c{#1{my@stop}}{#3}}%
                                          }%<<<
                                          letmyIfNoValueTFmy@ifmark
                                          letmyIfBooleanTFmy@ifmark
                                          makeatother
                                          % <<<

                                          % the sheet path parser >>>
                                          makeatletter
                                          definsertpath#1{edefsheetpath@{unexpandedexpandafter{sheetpath@#1}}}
                                          defsheetpathcurve#1#2#3#4%
                                          {%
                                          to[out=0,in=180] ++({.5*sheetlength},{#1*sheetheight})
                                          myIfBooleanTF{#3}{}{node[scale=sheetdotsize,inner sep=0pt]{.}}
                                          myIfNoValueTF{#4}{}{coordinate({#4})}
                                          to[out=0,in=180] ++({.5*sheetlength},{#2*sheetheight})
                                          }
                                          defoutputpath{drawsheetpath@;}
                                          defsheet{defsheetpath@{}myparserrun{sheet path}}
                                          makeatother
                                          myparserdef{sheet path}{initial}{the character (}[r,r)]
                                          {insertpath{({#1},{#2*sheetheight})}myparserstate{started}}
                                          myparserdef{sheet path}{initial}{the character =}
                                          {insertpath{(0,0)--++(sheetlength,0)}myparserstate{started}}
                                          myparserdef{sheet path}{started}{the character (}[r)]
                                          {insertpath{coordinate({#1})}}
                                          myparserdef{sheet path}{started}{the character =}
                                          {insertpath{--++(sheetlength,0)}}
                                          myparserdef{sheet path}{started}{the letter u}[txd()]
                                          {insertpath{sheetpathcurve{.5}{-.5}{#1}{#2}}}
                                          myparserdef{sheet path}{started}{the letter U}[txd()]
                                          {insertpath{sheetpathcurve{1}{-1}{#1}{#2}}}
                                          myparserdef{sheet path}{started}{the letter d}[txd()]
                                          {insertpath{sheetpathcurve{-.5}{.5}{#1}{#2}}}
                                          myparserdef{sheet path}{started}{the letter D}[txd()]
                                          {insertpath{sheetpathcurve{-1}{1}{#1}{#2}}}
                                          % making '.' a no-op, that way we can use it to end the search for an optional
                                          % argument for instance
                                          myparserdef{sheet path}{started} .{}
                                          myparserdef{sheet path}{started}{the letter x}[d()]
                                          {%
                                          myIfNoValueTF{#1}
                                          {%
                                          insertpath
                                          {--node[scale=sheetdotsize,inner sep=0pt]{.}++(sheetlength,0)}%
                                          }
                                          {%
                                          insertpath
                                          {%
                                          --node[scale=sheetdotsize,inner sep=0pt]{.}
                                          coordinate({#1})
                                          ++(sheetlength,0)
                                          }%
                                          }%
                                          }
                                          myparserdef{sheet path}{all}{the character ;}{myparserstate{final}outputpath}
                                          % <<<

                                          % sheet height and sheet length >>>
                                          pgfset
                                          {
                                          ,sheet height/.store in=sheetheight
                                          ,sheet height=1
                                          ,sheet length/.store in=sheetlength
                                          ,sheet length=1
                                          ,sheet dot size/.store in=sheetdotsize
                                          ,sheet dot size=4
                                          }
                                          %<<<

                                          begin{document}
                                          begin{tikzpicture}
                                          begin{scope}[thick, sheet height=0.75]
                                          sheet === ===d(sp1)=;
                                          sheet (0,-1) ==d(sp2)===ux =;
                                          sheet (0,-2) ==ux ===Dx =;
                                          sheet (0,-3) === ==== =;
                                          sheet (0,-4) === ===U(sp3)=;
                                          sheet (0,-5.5) ==x(b1) ===x(b2) =;
                                          end{scope}
                                          draw[dashed]
                                          (b2) -- (sp1)
                                          (b1) -- (sp2)
                                          ;
                                          end{tikzpicture}
                                          end{document}


                                          enter image description here







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                                          edited 18 hours ago

























                                          answered yesterday









                                          SkillmonSkillmon

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                                          • Wow ! This is a huge work. I'm impressed (like always I'm by the texperts ;)).

                                            – Kpym
                                            7 hours ago



















                                          • Wow ! This is a huge work. I'm impressed (like always I'm by the texperts ;)).

                                            – Kpym
                                            7 hours ago

















                                          Wow ! This is a huge work. I'm impressed (like always I'm by the texperts ;)).

                                          – Kpym
                                          7 hours ago





                                          Wow ! This is a huge work. I'm impressed (like always I'm by the texperts ;)).

                                          – Kpym
                                          7 hours ago


















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