Hcfyk

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}

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}

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}

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}

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}

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}