TikZ-decoration: control decoration amplitude along curve

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13















Working with path decorations based on this solution provided by marmot I am searching for a possibility to change the decorations amplitude along the graph.



Having this plot



enter image description here



applying the mentioned decoration gives



enter image description here



which is exactly what the decoration is supposed to do.



In fact the required curve should look like this one:



enter image description here



The last output has been created by manually searching the correct positions to manipulate the amplitude which is a "trial and error" method. Changing the dimensions of the tikzpicture will then give a false result, fx



enter image description here



Now the basic idea is to provide a separate path (which can be made visible during development) to control the decorations amplitude along the original (blue) curve. In this case the control path (red) would be quite simple:



enter image description here



The control path could be interpreted as a factor to the decorations amplitude that can be set via decoration=amplitude=.



Assuming this method would be quite handy I'm a bit stunned it is not available in TikZ - or have I overseen it? And if it's not: how can I get the y-value of the control curve within the statestep portion of the decorations definition?



The MWE producing all the above graphs (even if not nicely coded in terms of efficiency and structural beauty):



documentclassarticle
usepackagetikz
usetikzlibrarycalc,decorations.pathmorphing

newcounterrandymark
newcommandamplitudesetter
pgfdeclaredecorationmark random y stepsstart
%
statestart[width=+0pt,next state=step,persistent precomputation=pgfdecoratepathhascornerstruesetcounterrandymark0]
stepcounterrandymark
pgfcoordinaterandymarkarabicrandymarkpgfpoint0pt0pt
%
statestep[auto end on length=1.5pgfdecorationsegmentlength,
auto corner on length=1.5pgfdecorationsegmentlength,
width=+pgfdecorationsegmentlength]
stepcounterrandymarkamplitudesetter
pgfcoordinaterandymarkarabicrandymarkpgfpointpgfdecorationsegmentlengthrand*pgfdecorationsegmentamplitude
%
statefinal
stepcounterrandymark
pgfcoordinaterandymarkarabicrandymarkpgfpointdecoratedpathlast%
%
%

begindocument
begintikzpicture[x=5mm,y=5mm,decoration=mark random y steps,segment length=1.5mm,amplitude=0.75mm]% original curve
draw[style=help lines] (0,-4) grid[step=5mm] (25,1);
pgfmathsetseed2
draw[blue!80!black,thick] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
endtikzpicture

vspace2ex

begintikzpicture[x=5mm,y=5mm,decoration=mark random y steps,segment length=1.5mm,amplitude=0.75mm]% original curve
draw[style=help lines] (0,-4) grid[step=5mm] (25,1);
pgfmathsetseed2
draw[black] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
path[decorate] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
draw[blue!80!black,thick] plot[variable=x,samples at=1,...,arabicrandymark,smooth] (randymarkx);
endtikzpicture

vspace2ex

begintikzpicture[x=5mm,y=5mm,decoration=mark random y steps,segment length=1.5mm,amplitude=0.75mm]% original curve
draw[style=help lines] (0,-4) grid[step=5mm] (25,1);
pgfmathsetseed2
renewcommandamplitudesetter%
pgfdecorationsegmentamplitude=0.75mm
ifnumvaluerandymark<48pgfdecorationsegmentamplitude=0.7mmfi%
ifnumvaluerandymark<46pgfdecorationsegmentamplitude=0.6mmfi%
ifnumvaluerandymark<44pgfdecorationsegmentamplitude=0.5mmfi%
ifnumvaluerandymark<42pgfdecorationsegmentamplitude=0.4mmfi%
ifnumvaluerandymark<40pgfdecorationsegmentamplitude=0.3mmfi%
ifnumvaluerandymark<38pgfdecorationsegmentamplitude=0.2mmfi%
ifnumvaluerandymark<36pgfdecorationsegmentamplitude=0.1mmfi%
ifnumvaluerandymark<34pgfdecorationsegmentamplitude=0mmfi%
ifnumvaluerandymark<8pgfdecorationsegmentamplitude=0.75mmfi%

draw[black] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
path[decorate] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
draw[blue!80!black,thick] plot[variable=x,samples at=1,...,arabicrandymark,smooth] (randymarkx);
endtikzpicture

vspace2ex

begintikzpicture[x=2.5mm,y=2.5mm,decoration=mark random y steps,segment length=1.5mm,amplitude=0.75mm]% original curve
draw[style=help lines] (0,-4) grid[step=5mm] (25,1);
pgfmathsetseed2
renewcommandamplitudesetter%
pgfdecorationsegmentamplitude=0.75mm
ifnumvaluerandymark<48pgfdecorationsegmentamplitude=0.7mmfi%
ifnumvaluerandymark<46pgfdecorationsegmentamplitude=0.6mmfi%
ifnumvaluerandymark<44pgfdecorationsegmentamplitude=0.5mmfi%
ifnumvaluerandymark<42pgfdecorationsegmentamplitude=0.4mmfi%
ifnumvaluerandymark<40pgfdecorationsegmentamplitude=0.3mmfi%
ifnumvaluerandymark<38pgfdecorationsegmentamplitude=0.2mmfi%
ifnumvaluerandymark<36pgfdecorationsegmentamplitude=0.1mmfi%
ifnumvaluerandymark<34pgfdecorationsegmentamplitude=0mmfi%
ifnumvaluerandymark<8pgfdecorationsegmentamplitude=0.75mmfi%

draw[black] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
path[decorate] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
draw[blue!80!black,thick] plot[variable=x,samples at=1,...,arabicrandymark,smooth] (randymarkx);
endtikzpicture

vspace2ex

begintikzpicture[x=5mm,y=5mm,decoration=mark random y steps,segment length=1.5mm,amplitude=0.75mm]
draw[style=help lines] (0,-4) grid[step=5mm] (25,1);
pgfmathsetseed2
draw [red,thick,name=amplitudecontrol] (0,1) -- (2,1) -- (2,0) -- (7,0) -- (12,1) -- (25,1);
draw[blue!80!black,thick] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
endtikzpicture

enddocument









share|improve this question


























    13















    Working with path decorations based on this solution provided by marmot I am searching for a possibility to change the decorations amplitude along the graph.



    Having this plot



    enter image description here



    applying the mentioned decoration gives



    enter image description here



    which is exactly what the decoration is supposed to do.



    In fact the required curve should look like this one:



    enter image description here



    The last output has been created by manually searching the correct positions to manipulate the amplitude which is a "trial and error" method. Changing the dimensions of the tikzpicture will then give a false result, fx



    enter image description here



    Now the basic idea is to provide a separate path (which can be made visible during development) to control the decorations amplitude along the original (blue) curve. In this case the control path (red) would be quite simple:



    enter image description here



    The control path could be interpreted as a factor to the decorations amplitude that can be set via decoration=amplitude=.



    Assuming this method would be quite handy I'm a bit stunned it is not available in TikZ - or have I overseen it? And if it's not: how can I get the y-value of the control curve within the statestep portion of the decorations definition?



    The MWE producing all the above graphs (even if not nicely coded in terms of efficiency and structural beauty):



    documentclassarticle
    usepackagetikz
    usetikzlibrarycalc,decorations.pathmorphing

    newcounterrandymark
    newcommandamplitudesetter
    pgfdeclaredecorationmark random y stepsstart
    %
    statestart[width=+0pt,next state=step,persistent precomputation=pgfdecoratepathhascornerstruesetcounterrandymark0]
    stepcounterrandymark
    pgfcoordinaterandymarkarabicrandymarkpgfpoint0pt0pt
    %
    statestep[auto end on length=1.5pgfdecorationsegmentlength,
    auto corner on length=1.5pgfdecorationsegmentlength,
    width=+pgfdecorationsegmentlength]
    stepcounterrandymarkamplitudesetter
    pgfcoordinaterandymarkarabicrandymarkpgfpointpgfdecorationsegmentlengthrand*pgfdecorationsegmentamplitude
    %
    statefinal
    stepcounterrandymark
    pgfcoordinaterandymarkarabicrandymarkpgfpointdecoratedpathlast%
    %
    %

    begindocument
    begintikzpicture[x=5mm,y=5mm,decoration=mark random y steps,segment length=1.5mm,amplitude=0.75mm]% original curve
    draw[style=help lines] (0,-4) grid[step=5mm] (25,1);
    pgfmathsetseed2
    draw[blue!80!black,thick] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
    endtikzpicture

    vspace2ex

    begintikzpicture[x=5mm,y=5mm,decoration=mark random y steps,segment length=1.5mm,amplitude=0.75mm]% original curve
    draw[style=help lines] (0,-4) grid[step=5mm] (25,1);
    pgfmathsetseed2
    draw[black] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
    path[decorate] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
    draw[blue!80!black,thick] plot[variable=x,samples at=1,...,arabicrandymark,smooth] (randymarkx);
    endtikzpicture

    vspace2ex

    begintikzpicture[x=5mm,y=5mm,decoration=mark random y steps,segment length=1.5mm,amplitude=0.75mm]% original curve
    draw[style=help lines] (0,-4) grid[step=5mm] (25,1);
    pgfmathsetseed2
    renewcommandamplitudesetter%
    pgfdecorationsegmentamplitude=0.75mm
    ifnumvaluerandymark<48pgfdecorationsegmentamplitude=0.7mmfi%
    ifnumvaluerandymark<46pgfdecorationsegmentamplitude=0.6mmfi%
    ifnumvaluerandymark<44pgfdecorationsegmentamplitude=0.5mmfi%
    ifnumvaluerandymark<42pgfdecorationsegmentamplitude=0.4mmfi%
    ifnumvaluerandymark<40pgfdecorationsegmentamplitude=0.3mmfi%
    ifnumvaluerandymark<38pgfdecorationsegmentamplitude=0.2mmfi%
    ifnumvaluerandymark<36pgfdecorationsegmentamplitude=0.1mmfi%
    ifnumvaluerandymark<34pgfdecorationsegmentamplitude=0mmfi%
    ifnumvaluerandymark<8pgfdecorationsegmentamplitude=0.75mmfi%

    draw[black] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
    path[decorate] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
    draw[blue!80!black,thick] plot[variable=x,samples at=1,...,arabicrandymark,smooth] (randymarkx);
    endtikzpicture

    vspace2ex

    begintikzpicture[x=2.5mm,y=2.5mm,decoration=mark random y steps,segment length=1.5mm,amplitude=0.75mm]% original curve
    draw[style=help lines] (0,-4) grid[step=5mm] (25,1);
    pgfmathsetseed2
    renewcommandamplitudesetter%
    pgfdecorationsegmentamplitude=0.75mm
    ifnumvaluerandymark<48pgfdecorationsegmentamplitude=0.7mmfi%
    ifnumvaluerandymark<46pgfdecorationsegmentamplitude=0.6mmfi%
    ifnumvaluerandymark<44pgfdecorationsegmentamplitude=0.5mmfi%
    ifnumvaluerandymark<42pgfdecorationsegmentamplitude=0.4mmfi%
    ifnumvaluerandymark<40pgfdecorationsegmentamplitude=0.3mmfi%
    ifnumvaluerandymark<38pgfdecorationsegmentamplitude=0.2mmfi%
    ifnumvaluerandymark<36pgfdecorationsegmentamplitude=0.1mmfi%
    ifnumvaluerandymark<34pgfdecorationsegmentamplitude=0mmfi%
    ifnumvaluerandymark<8pgfdecorationsegmentamplitude=0.75mmfi%

    draw[black] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
    path[decorate] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
    draw[blue!80!black,thick] plot[variable=x,samples at=1,...,arabicrandymark,smooth] (randymarkx);
    endtikzpicture

    vspace2ex

    begintikzpicture[x=5mm,y=5mm,decoration=mark random y steps,segment length=1.5mm,amplitude=0.75mm]
    draw[style=help lines] (0,-4) grid[step=5mm] (25,1);
    pgfmathsetseed2
    draw [red,thick,name=amplitudecontrol] (0,1) -- (2,1) -- (2,0) -- (7,0) -- (12,1) -- (25,1);
    draw[blue!80!black,thick] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
    endtikzpicture

    enddocument









    share|improve this question
























      13












      13








      13


      1






      Working with path decorations based on this solution provided by marmot I am searching for a possibility to change the decorations amplitude along the graph.



      Having this plot



      enter image description here



      applying the mentioned decoration gives



      enter image description here



      which is exactly what the decoration is supposed to do.



      In fact the required curve should look like this one:



      enter image description here



      The last output has been created by manually searching the correct positions to manipulate the amplitude which is a "trial and error" method. Changing the dimensions of the tikzpicture will then give a false result, fx



      enter image description here



      Now the basic idea is to provide a separate path (which can be made visible during development) to control the decorations amplitude along the original (blue) curve. In this case the control path (red) would be quite simple:



      enter image description here



      The control path could be interpreted as a factor to the decorations amplitude that can be set via decoration=amplitude=.



      Assuming this method would be quite handy I'm a bit stunned it is not available in TikZ - or have I overseen it? And if it's not: how can I get the y-value of the control curve within the statestep portion of the decorations definition?



      The MWE producing all the above graphs (even if not nicely coded in terms of efficiency and structural beauty):



      documentclassarticle
      usepackagetikz
      usetikzlibrarycalc,decorations.pathmorphing

      newcounterrandymark
      newcommandamplitudesetter
      pgfdeclaredecorationmark random y stepsstart
      %
      statestart[width=+0pt,next state=step,persistent precomputation=pgfdecoratepathhascornerstruesetcounterrandymark0]
      stepcounterrandymark
      pgfcoordinaterandymarkarabicrandymarkpgfpoint0pt0pt
      %
      statestep[auto end on length=1.5pgfdecorationsegmentlength,
      auto corner on length=1.5pgfdecorationsegmentlength,
      width=+pgfdecorationsegmentlength]
      stepcounterrandymarkamplitudesetter
      pgfcoordinaterandymarkarabicrandymarkpgfpointpgfdecorationsegmentlengthrand*pgfdecorationsegmentamplitude
      %
      statefinal
      stepcounterrandymark
      pgfcoordinaterandymarkarabicrandymarkpgfpointdecoratedpathlast%
      %
      %

      begindocument
      begintikzpicture[x=5mm,y=5mm,decoration=mark random y steps,segment length=1.5mm,amplitude=0.75mm]% original curve
      draw[style=help lines] (0,-4) grid[step=5mm] (25,1);
      pgfmathsetseed2
      draw[blue!80!black,thick] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
      endtikzpicture

      vspace2ex

      begintikzpicture[x=5mm,y=5mm,decoration=mark random y steps,segment length=1.5mm,amplitude=0.75mm]% original curve
      draw[style=help lines] (0,-4) grid[step=5mm] (25,1);
      pgfmathsetseed2
      draw[black] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
      path[decorate] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
      draw[blue!80!black,thick] plot[variable=x,samples at=1,...,arabicrandymark,smooth] (randymarkx);
      endtikzpicture

      vspace2ex

      begintikzpicture[x=5mm,y=5mm,decoration=mark random y steps,segment length=1.5mm,amplitude=0.75mm]% original curve
      draw[style=help lines] (0,-4) grid[step=5mm] (25,1);
      pgfmathsetseed2
      renewcommandamplitudesetter%
      pgfdecorationsegmentamplitude=0.75mm
      ifnumvaluerandymark<48pgfdecorationsegmentamplitude=0.7mmfi%
      ifnumvaluerandymark<46pgfdecorationsegmentamplitude=0.6mmfi%
      ifnumvaluerandymark<44pgfdecorationsegmentamplitude=0.5mmfi%
      ifnumvaluerandymark<42pgfdecorationsegmentamplitude=0.4mmfi%
      ifnumvaluerandymark<40pgfdecorationsegmentamplitude=0.3mmfi%
      ifnumvaluerandymark<38pgfdecorationsegmentamplitude=0.2mmfi%
      ifnumvaluerandymark<36pgfdecorationsegmentamplitude=0.1mmfi%
      ifnumvaluerandymark<34pgfdecorationsegmentamplitude=0mmfi%
      ifnumvaluerandymark<8pgfdecorationsegmentamplitude=0.75mmfi%

      draw[black] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
      path[decorate] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
      draw[blue!80!black,thick] plot[variable=x,samples at=1,...,arabicrandymark,smooth] (randymarkx);
      endtikzpicture

      vspace2ex

      begintikzpicture[x=2.5mm,y=2.5mm,decoration=mark random y steps,segment length=1.5mm,amplitude=0.75mm]% original curve
      draw[style=help lines] (0,-4) grid[step=5mm] (25,1);
      pgfmathsetseed2
      renewcommandamplitudesetter%
      pgfdecorationsegmentamplitude=0.75mm
      ifnumvaluerandymark<48pgfdecorationsegmentamplitude=0.7mmfi%
      ifnumvaluerandymark<46pgfdecorationsegmentamplitude=0.6mmfi%
      ifnumvaluerandymark<44pgfdecorationsegmentamplitude=0.5mmfi%
      ifnumvaluerandymark<42pgfdecorationsegmentamplitude=0.4mmfi%
      ifnumvaluerandymark<40pgfdecorationsegmentamplitude=0.3mmfi%
      ifnumvaluerandymark<38pgfdecorationsegmentamplitude=0.2mmfi%
      ifnumvaluerandymark<36pgfdecorationsegmentamplitude=0.1mmfi%
      ifnumvaluerandymark<34pgfdecorationsegmentamplitude=0mmfi%
      ifnumvaluerandymark<8pgfdecorationsegmentamplitude=0.75mmfi%

      draw[black] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
      path[decorate] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
      draw[blue!80!black,thick] plot[variable=x,samples at=1,...,arabicrandymark,smooth] (randymarkx);
      endtikzpicture

      vspace2ex

      begintikzpicture[x=5mm,y=5mm,decoration=mark random y steps,segment length=1.5mm,amplitude=0.75mm]
      draw[style=help lines] (0,-4) grid[step=5mm] (25,1);
      pgfmathsetseed2
      draw [red,thick,name=amplitudecontrol] (0,1) -- (2,1) -- (2,0) -- (7,0) -- (12,1) -- (25,1);
      draw[blue!80!black,thick] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
      endtikzpicture

      enddocument









      share|improve this question














      Working with path decorations based on this solution provided by marmot I am searching for a possibility to change the decorations amplitude along the graph.



      Having this plot



      enter image description here



      applying the mentioned decoration gives



      enter image description here



      which is exactly what the decoration is supposed to do.



      In fact the required curve should look like this one:



      enter image description here



      The last output has been created by manually searching the correct positions to manipulate the amplitude which is a "trial and error" method. Changing the dimensions of the tikzpicture will then give a false result, fx



      enter image description here



      Now the basic idea is to provide a separate path (which can be made visible during development) to control the decorations amplitude along the original (blue) curve. In this case the control path (red) would be quite simple:



      enter image description here



      The control path could be interpreted as a factor to the decorations amplitude that can be set via decoration=amplitude=.



      Assuming this method would be quite handy I'm a bit stunned it is not available in TikZ - or have I overseen it? And if it's not: how can I get the y-value of the control curve within the statestep portion of the decorations definition?



      The MWE producing all the above graphs (even if not nicely coded in terms of efficiency and structural beauty):



      documentclassarticle
      usepackagetikz
      usetikzlibrarycalc,decorations.pathmorphing

      newcounterrandymark
      newcommandamplitudesetter
      pgfdeclaredecorationmark random y stepsstart
      %
      statestart[width=+0pt,next state=step,persistent precomputation=pgfdecoratepathhascornerstruesetcounterrandymark0]
      stepcounterrandymark
      pgfcoordinaterandymarkarabicrandymarkpgfpoint0pt0pt
      %
      statestep[auto end on length=1.5pgfdecorationsegmentlength,
      auto corner on length=1.5pgfdecorationsegmentlength,
      width=+pgfdecorationsegmentlength]
      stepcounterrandymarkamplitudesetter
      pgfcoordinaterandymarkarabicrandymarkpgfpointpgfdecorationsegmentlengthrand*pgfdecorationsegmentamplitude
      %
      statefinal
      stepcounterrandymark
      pgfcoordinaterandymarkarabicrandymarkpgfpointdecoratedpathlast%
      %
      %

      begindocument
      begintikzpicture[x=5mm,y=5mm,decoration=mark random y steps,segment length=1.5mm,amplitude=0.75mm]% original curve
      draw[style=help lines] (0,-4) grid[step=5mm] (25,1);
      pgfmathsetseed2
      draw[blue!80!black,thick] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
      endtikzpicture

      vspace2ex

      begintikzpicture[x=5mm,y=5mm,decoration=mark random y steps,segment length=1.5mm,amplitude=0.75mm]% original curve
      draw[style=help lines] (0,-4) grid[step=5mm] (25,1);
      pgfmathsetseed2
      draw[black] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
      path[decorate] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
      draw[blue!80!black,thick] plot[variable=x,samples at=1,...,arabicrandymark,smooth] (randymarkx);
      endtikzpicture

      vspace2ex

      begintikzpicture[x=5mm,y=5mm,decoration=mark random y steps,segment length=1.5mm,amplitude=0.75mm]% original curve
      draw[style=help lines] (0,-4) grid[step=5mm] (25,1);
      pgfmathsetseed2
      renewcommandamplitudesetter%
      pgfdecorationsegmentamplitude=0.75mm
      ifnumvaluerandymark<48pgfdecorationsegmentamplitude=0.7mmfi%
      ifnumvaluerandymark<46pgfdecorationsegmentamplitude=0.6mmfi%
      ifnumvaluerandymark<44pgfdecorationsegmentamplitude=0.5mmfi%
      ifnumvaluerandymark<42pgfdecorationsegmentamplitude=0.4mmfi%
      ifnumvaluerandymark<40pgfdecorationsegmentamplitude=0.3mmfi%
      ifnumvaluerandymark<38pgfdecorationsegmentamplitude=0.2mmfi%
      ifnumvaluerandymark<36pgfdecorationsegmentamplitude=0.1mmfi%
      ifnumvaluerandymark<34pgfdecorationsegmentamplitude=0mmfi%
      ifnumvaluerandymark<8pgfdecorationsegmentamplitude=0.75mmfi%

      draw[black] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
      path[decorate] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
      draw[blue!80!black,thick] plot[variable=x,samples at=1,...,arabicrandymark,smooth] (randymarkx);
      endtikzpicture

      vspace2ex

      begintikzpicture[x=2.5mm,y=2.5mm,decoration=mark random y steps,segment length=1.5mm,amplitude=0.75mm]% original curve
      draw[style=help lines] (0,-4) grid[step=5mm] (25,1);
      pgfmathsetseed2
      renewcommandamplitudesetter%
      pgfdecorationsegmentamplitude=0.75mm
      ifnumvaluerandymark<48pgfdecorationsegmentamplitude=0.7mmfi%
      ifnumvaluerandymark<46pgfdecorationsegmentamplitude=0.6mmfi%
      ifnumvaluerandymark<44pgfdecorationsegmentamplitude=0.5mmfi%
      ifnumvaluerandymark<42pgfdecorationsegmentamplitude=0.4mmfi%
      ifnumvaluerandymark<40pgfdecorationsegmentamplitude=0.3mmfi%
      ifnumvaluerandymark<38pgfdecorationsegmentamplitude=0.2mmfi%
      ifnumvaluerandymark<36pgfdecorationsegmentamplitude=0.1mmfi%
      ifnumvaluerandymark<34pgfdecorationsegmentamplitude=0mmfi%
      ifnumvaluerandymark<8pgfdecorationsegmentamplitude=0.75mmfi%

      draw[black] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
      path[decorate] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
      draw[blue!80!black,thick] plot[variable=x,samples at=1,...,arabicrandymark,smooth] (randymarkx);
      endtikzpicture

      vspace2ex

      begintikzpicture[x=5mm,y=5mm,decoration=mark random y steps,segment length=1.5mm,amplitude=0.75mm]
      draw[style=help lines] (0,-4) grid[step=5mm] (25,1);
      pgfmathsetseed2
      draw [red,thick,name=amplitudecontrol] (0,1) -- (2,1) -- (2,0) -- (7,0) -- (12,1) -- (25,1);
      draw[blue!80!black,thick] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
      endtikzpicture

      enddocument






      tikz-pgf decorations tikz-decorations






      share|improve this question













      share|improve this question











      share|improve this question




      share|improve this question










      asked Mar 17 at 11:27









      AndiWAndiW

      3961213




      3961213




















          1 Answer
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          14














          Let me start by saying that I really like that question and am truly impressed by what you have achieved. Here is a proposal to address the scalability. Define a function that governs the amplitude,



          varyingamp(x) = whatever you like


          where x is the fraction of the decorated path (in order to ensure scalability). (Such a function has been used already here in order to have variable varying line widths. I would not at all be surprised if similar things had been used before.) This is the MWE.



          documentclassarticle
          usepackagetikz
          usetikzlibrarycalc,decorations.pathmorphing

          newcounterrandymark
          %newcommandamplitudesetter
          pgfdeclaredecorationmark random y stepsstart
          %
          statestart[width=+0pt,next state=step,persistent precomputation=
          pgfdecoratepathhascornerstruesetcounterrandymark0]
          stepcounterrandymark
          pgfcoordinaterandymarkarabicrandymarkpgfpoint0pt0pt
          %
          statestep[auto end on length=1.5pgfdecorationsegmentlength,
          auto corner on length=1.5pgfdecorationsegmentlength,
          width=+pgfdecorationsegmentlength]
          stepcounterrandymark%amplitudesetter
          pgfcoordinaterandymarkarabicrandymarkpgfpointpgfdecorationsegmentlengthrand*pgfdecorationsegmentamplitude
          %
          statefinal
          stepcounterrandymark
          pgfcoordinaterandymarkarabicrandymarkpgfpointdecoratedpathlast%
          %
          %

          pgfdeclaredecorationmark varying random y stepsstart
          %
          statestart[width=+0pt,next state=step,persistent precomputation=
          pgfdecoratepathhascornerstruesetcounterrandymark0]
          stepcounterrandymark
          pgfcoordinaterandymarkarabicrandymarkpgfpoint0pt0pt
          %
          statestep[auto end on length=1.5pgfdecorationsegmentlength,
          auto corner on length=1.5pgfdecorationsegmentlength,
          width=+pgfdecorationsegmentlength]
          stepcounterrandymark
          pgfmathsetmacromyfractionthepgfdecorationsegmentlength*valuerandymark/pgfdecoratedpathlength
          pgfmathsetmacromyamplitudevaryingamp(myfraction)
          %typeoutmyfraction,myamplitude
          pgfcoordinaterandymarkarabicrandymarkpgfpointpgfdecorationsegmentlengthrand*myamplitude*pgfdecorationsegmentamplitude
          %
          statefinal
          stepcounterrandymark
          pgfcoordinaterandymarkarabicrandymarkpgfpointdecoratedpathlast%
          %
          %



          begindocument
          begintikzpicture[x=5mm,y=5mm,decoration=mark random y steps,segment length=1.5mm,amplitude=0.75mm]% original curve
          draw[style=help lines] (0,-4) grid[step=5mm] (25,1);
          pgfmathsetseed2
          draw[blue!80!black,thick] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
          endtikzpicture

          vspace2ex

          begintikzpicture[x=5mm,y=5mm,decoration=mark varying random y steps,segment
          length=1.5mm,amplitude=0.75mm,declare function=
          varyingamp(x)=ifthenelse(x<0.08,1,ifthenelse(x<0.28,0,ifthenelse(x<0.48,5*(x-0.28),1)));]%
          draw[style=help lines] (0,-4) grid[step=5mm] (25,1);
          draw[red,thick] plot[variable=x,domain=0:25,samples=101] (x,varyingamp(x/25));
          pgfmathsetseed2
          draw[black] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
          path[decorate] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
          draw[blue!80!black,thick] plot[variable=x,samples at=1,...,arabicrandymark,smooth] (randymarkx);
          endtikzpicture

          vspace2ex

          begintikzpicture[x=2.5mm,y=2.5mm,decoration=mark varying random y
          steps,segment length=0.75mm,amplitude=0.75mm,declare function=
          varyingamp(x)=ifthenelse(x<0.08,1,ifthenelse(x<0.28,0,ifthenelse(x<0.48,5*(x-0.28),1)));]
          draw[style=help lines] (0,-4) grid[step=5mm] (25,1);
          pgfmathsetseed2
          draw[black] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
          path[decorate] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
          draw[blue!80!black,thick] plot[variable=x,samples at=1,...,arabicrandymark,smooth] (randymarkx);
          endtikzpicture
          enddocument


          enter image description here



          The function is shown in red in the second plot. The third plot shows scalability. (Of course, you also need to rescale the segment lengths. Notice also that this decoration has discrete steps, so if you have a strongly varying function but only a few steps, the function may not be fully "appreciated" since it only gets evaluated at a few points.)






          share|improve this answer


















          • 1





            +1 for this amazing answer, and I wish I could +1 another time for the first sentence only...

            – JouleV
            Mar 17 at 16:03











          • @marmot you know you're driving me crazy, don't you? I did not even get a basic function implemented yet and you, well, uh. Ok, I'm digging through this one. Btw: x holds the fraction of pgfdecoratedpathlength, right? Even if your approach is more elegant than mine it's not the red curve that controls the amplitude... Therefore I would like to keep the question still open if you don't mind...

            – AndiW
            Mar 17 at 16:35






          • 1





            @AndiW Sorry for driving you crazy. ;-) The function drawn in red does determine the amplitude, i.e. the random deviation is rand*varyingamp(s)*pgfdecorationsegmentamplitude, where s denotes the fraction of the path we are at. Of course, s is not the x value of the curve at that point, which would not be independent of the coordinate system. You could of course define your own function that returns the path length s (or fraction) a a function of x, which would work in this specific case because here it is single-valued but in general it is not. (I'm just back from cycling.... )

            – marmot
            Mar 17 at 18:37






          • 1





            @AndiW Yes. What you are saying is correct, but is not contradicting with any of my statements, is it?

            – marmot
            Mar 17 at 20:21






          • 1





            @marmot well - actually I sometimes forget that LaTeX is no low-level-end-user tool. Given the fact that it's a function controling the amplitude and not a graph (which would be something an end-user would expect) the answer is great. Having quit physics 25 yrs ago I have to change my approach I guess... :-) +1!

            – AndiW
            Mar 17 at 21:04











          Your Answer








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          1 Answer
          1






          active

          oldest

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          1 Answer
          1






          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes









          14














          Let me start by saying that I really like that question and am truly impressed by what you have achieved. Here is a proposal to address the scalability. Define a function that governs the amplitude,



          varyingamp(x) = whatever you like


          where x is the fraction of the decorated path (in order to ensure scalability). (Such a function has been used already here in order to have variable varying line widths. I would not at all be surprised if similar things had been used before.) This is the MWE.



          documentclassarticle
          usepackagetikz
          usetikzlibrarycalc,decorations.pathmorphing

          newcounterrandymark
          %newcommandamplitudesetter
          pgfdeclaredecorationmark random y stepsstart
          %
          statestart[width=+0pt,next state=step,persistent precomputation=
          pgfdecoratepathhascornerstruesetcounterrandymark0]
          stepcounterrandymark
          pgfcoordinaterandymarkarabicrandymarkpgfpoint0pt0pt
          %
          statestep[auto end on length=1.5pgfdecorationsegmentlength,
          auto corner on length=1.5pgfdecorationsegmentlength,
          width=+pgfdecorationsegmentlength]
          stepcounterrandymark%amplitudesetter
          pgfcoordinaterandymarkarabicrandymarkpgfpointpgfdecorationsegmentlengthrand*pgfdecorationsegmentamplitude
          %
          statefinal
          stepcounterrandymark
          pgfcoordinaterandymarkarabicrandymarkpgfpointdecoratedpathlast%
          %
          %

          pgfdeclaredecorationmark varying random y stepsstart
          %
          statestart[width=+0pt,next state=step,persistent precomputation=
          pgfdecoratepathhascornerstruesetcounterrandymark0]
          stepcounterrandymark
          pgfcoordinaterandymarkarabicrandymarkpgfpoint0pt0pt
          %
          statestep[auto end on length=1.5pgfdecorationsegmentlength,
          auto corner on length=1.5pgfdecorationsegmentlength,
          width=+pgfdecorationsegmentlength]
          stepcounterrandymark
          pgfmathsetmacromyfractionthepgfdecorationsegmentlength*valuerandymark/pgfdecoratedpathlength
          pgfmathsetmacromyamplitudevaryingamp(myfraction)
          %typeoutmyfraction,myamplitude
          pgfcoordinaterandymarkarabicrandymarkpgfpointpgfdecorationsegmentlengthrand*myamplitude*pgfdecorationsegmentamplitude
          %
          statefinal
          stepcounterrandymark
          pgfcoordinaterandymarkarabicrandymarkpgfpointdecoratedpathlast%
          %
          %



          begindocument
          begintikzpicture[x=5mm,y=5mm,decoration=mark random y steps,segment length=1.5mm,amplitude=0.75mm]% original curve
          draw[style=help lines] (0,-4) grid[step=5mm] (25,1);
          pgfmathsetseed2
          draw[blue!80!black,thick] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
          endtikzpicture

          vspace2ex

          begintikzpicture[x=5mm,y=5mm,decoration=mark varying random y steps,segment
          length=1.5mm,amplitude=0.75mm,declare function=
          varyingamp(x)=ifthenelse(x<0.08,1,ifthenelse(x<0.28,0,ifthenelse(x<0.48,5*(x-0.28),1)));]%
          draw[style=help lines] (0,-4) grid[step=5mm] (25,1);
          draw[red,thick] plot[variable=x,domain=0:25,samples=101] (x,varyingamp(x/25));
          pgfmathsetseed2
          draw[black] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
          path[decorate] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
          draw[blue!80!black,thick] plot[variable=x,samples at=1,...,arabicrandymark,smooth] (randymarkx);
          endtikzpicture

          vspace2ex

          begintikzpicture[x=2.5mm,y=2.5mm,decoration=mark varying random y
          steps,segment length=0.75mm,amplitude=0.75mm,declare function=
          varyingamp(x)=ifthenelse(x<0.08,1,ifthenelse(x<0.28,0,ifthenelse(x<0.48,5*(x-0.28),1)));]
          draw[style=help lines] (0,-4) grid[step=5mm] (25,1);
          pgfmathsetseed2
          draw[black] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
          path[decorate] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
          draw[blue!80!black,thick] plot[variable=x,samples at=1,...,arabicrandymark,smooth] (randymarkx);
          endtikzpicture
          enddocument


          enter image description here



          The function is shown in red in the second plot. The third plot shows scalability. (Of course, you also need to rescale the segment lengths. Notice also that this decoration has discrete steps, so if you have a strongly varying function but only a few steps, the function may not be fully "appreciated" since it only gets evaluated at a few points.)






          share|improve this answer


















          • 1





            +1 for this amazing answer, and I wish I could +1 another time for the first sentence only...

            – JouleV
            Mar 17 at 16:03











          • @marmot you know you're driving me crazy, don't you? I did not even get a basic function implemented yet and you, well, uh. Ok, I'm digging through this one. Btw: x holds the fraction of pgfdecoratedpathlength, right? Even if your approach is more elegant than mine it's not the red curve that controls the amplitude... Therefore I would like to keep the question still open if you don't mind...

            – AndiW
            Mar 17 at 16:35






          • 1





            @AndiW Sorry for driving you crazy. ;-) The function drawn in red does determine the amplitude, i.e. the random deviation is rand*varyingamp(s)*pgfdecorationsegmentamplitude, where s denotes the fraction of the path we are at. Of course, s is not the x value of the curve at that point, which would not be independent of the coordinate system. You could of course define your own function that returns the path length s (or fraction) a a function of x, which would work in this specific case because here it is single-valued but in general it is not. (I'm just back from cycling.... )

            – marmot
            Mar 17 at 18:37






          • 1





            @AndiW Yes. What you are saying is correct, but is not contradicting with any of my statements, is it?

            – marmot
            Mar 17 at 20:21






          • 1





            @marmot well - actually I sometimes forget that LaTeX is no low-level-end-user tool. Given the fact that it's a function controling the amplitude and not a graph (which would be something an end-user would expect) the answer is great. Having quit physics 25 yrs ago I have to change my approach I guess... :-) +1!

            – AndiW
            Mar 17 at 21:04















          14














          Let me start by saying that I really like that question and am truly impressed by what you have achieved. Here is a proposal to address the scalability. Define a function that governs the amplitude,



          varyingamp(x) = whatever you like


          where x is the fraction of the decorated path (in order to ensure scalability). (Such a function has been used already here in order to have variable varying line widths. I would not at all be surprised if similar things had been used before.) This is the MWE.



          documentclassarticle
          usepackagetikz
          usetikzlibrarycalc,decorations.pathmorphing

          newcounterrandymark
          %newcommandamplitudesetter
          pgfdeclaredecorationmark random y stepsstart
          %
          statestart[width=+0pt,next state=step,persistent precomputation=
          pgfdecoratepathhascornerstruesetcounterrandymark0]
          stepcounterrandymark
          pgfcoordinaterandymarkarabicrandymarkpgfpoint0pt0pt
          %
          statestep[auto end on length=1.5pgfdecorationsegmentlength,
          auto corner on length=1.5pgfdecorationsegmentlength,
          width=+pgfdecorationsegmentlength]
          stepcounterrandymark%amplitudesetter
          pgfcoordinaterandymarkarabicrandymarkpgfpointpgfdecorationsegmentlengthrand*pgfdecorationsegmentamplitude
          %
          statefinal
          stepcounterrandymark
          pgfcoordinaterandymarkarabicrandymarkpgfpointdecoratedpathlast%
          %
          %

          pgfdeclaredecorationmark varying random y stepsstart
          %
          statestart[width=+0pt,next state=step,persistent precomputation=
          pgfdecoratepathhascornerstruesetcounterrandymark0]
          stepcounterrandymark
          pgfcoordinaterandymarkarabicrandymarkpgfpoint0pt0pt
          %
          statestep[auto end on length=1.5pgfdecorationsegmentlength,
          auto corner on length=1.5pgfdecorationsegmentlength,
          width=+pgfdecorationsegmentlength]
          stepcounterrandymark
          pgfmathsetmacromyfractionthepgfdecorationsegmentlength*valuerandymark/pgfdecoratedpathlength
          pgfmathsetmacromyamplitudevaryingamp(myfraction)
          %typeoutmyfraction,myamplitude
          pgfcoordinaterandymarkarabicrandymarkpgfpointpgfdecorationsegmentlengthrand*myamplitude*pgfdecorationsegmentamplitude
          %
          statefinal
          stepcounterrandymark
          pgfcoordinaterandymarkarabicrandymarkpgfpointdecoratedpathlast%
          %
          %



          begindocument
          begintikzpicture[x=5mm,y=5mm,decoration=mark random y steps,segment length=1.5mm,amplitude=0.75mm]% original curve
          draw[style=help lines] (0,-4) grid[step=5mm] (25,1);
          pgfmathsetseed2
          draw[blue!80!black,thick] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
          endtikzpicture

          vspace2ex

          begintikzpicture[x=5mm,y=5mm,decoration=mark varying random y steps,segment
          length=1.5mm,amplitude=0.75mm,declare function=
          varyingamp(x)=ifthenelse(x<0.08,1,ifthenelse(x<0.28,0,ifthenelse(x<0.48,5*(x-0.28),1)));]%
          draw[style=help lines] (0,-4) grid[step=5mm] (25,1);
          draw[red,thick] plot[variable=x,domain=0:25,samples=101] (x,varyingamp(x/25));
          pgfmathsetseed2
          draw[black] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
          path[decorate] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
          draw[blue!80!black,thick] plot[variable=x,samples at=1,...,arabicrandymark,smooth] (randymarkx);
          endtikzpicture

          vspace2ex

          begintikzpicture[x=2.5mm,y=2.5mm,decoration=mark varying random y
          steps,segment length=0.75mm,amplitude=0.75mm,declare function=
          varyingamp(x)=ifthenelse(x<0.08,1,ifthenelse(x<0.28,0,ifthenelse(x<0.48,5*(x-0.28),1)));]
          draw[style=help lines] (0,-4) grid[step=5mm] (25,1);
          pgfmathsetseed2
          draw[black] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
          path[decorate] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
          draw[blue!80!black,thick] plot[variable=x,samples at=1,...,arabicrandymark,smooth] (randymarkx);
          endtikzpicture
          enddocument


          enter image description here



          The function is shown in red in the second plot. The third plot shows scalability. (Of course, you also need to rescale the segment lengths. Notice also that this decoration has discrete steps, so if you have a strongly varying function but only a few steps, the function may not be fully "appreciated" since it only gets evaluated at a few points.)






          share|improve this answer


















          • 1





            +1 for this amazing answer, and I wish I could +1 another time for the first sentence only...

            – JouleV
            Mar 17 at 16:03











          • @marmot you know you're driving me crazy, don't you? I did not even get a basic function implemented yet and you, well, uh. Ok, I'm digging through this one. Btw: x holds the fraction of pgfdecoratedpathlength, right? Even if your approach is more elegant than mine it's not the red curve that controls the amplitude... Therefore I would like to keep the question still open if you don't mind...

            – AndiW
            Mar 17 at 16:35






          • 1





            @AndiW Sorry for driving you crazy. ;-) The function drawn in red does determine the amplitude, i.e. the random deviation is rand*varyingamp(s)*pgfdecorationsegmentamplitude, where s denotes the fraction of the path we are at. Of course, s is not the x value of the curve at that point, which would not be independent of the coordinate system. You could of course define your own function that returns the path length s (or fraction) a a function of x, which would work in this specific case because here it is single-valued but in general it is not. (I'm just back from cycling.... )

            – marmot
            Mar 17 at 18:37






          • 1





            @AndiW Yes. What you are saying is correct, but is not contradicting with any of my statements, is it?

            – marmot
            Mar 17 at 20:21






          • 1





            @marmot well - actually I sometimes forget that LaTeX is no low-level-end-user tool. Given the fact that it's a function controling the amplitude and not a graph (which would be something an end-user would expect) the answer is great. Having quit physics 25 yrs ago I have to change my approach I guess... :-) +1!

            – AndiW
            Mar 17 at 21:04













          14












          14








          14







          Let me start by saying that I really like that question and am truly impressed by what you have achieved. Here is a proposal to address the scalability. Define a function that governs the amplitude,



          varyingamp(x) = whatever you like


          where x is the fraction of the decorated path (in order to ensure scalability). (Such a function has been used already here in order to have variable varying line widths. I would not at all be surprised if similar things had been used before.) This is the MWE.



          documentclassarticle
          usepackagetikz
          usetikzlibrarycalc,decorations.pathmorphing

          newcounterrandymark
          %newcommandamplitudesetter
          pgfdeclaredecorationmark random y stepsstart
          %
          statestart[width=+0pt,next state=step,persistent precomputation=
          pgfdecoratepathhascornerstruesetcounterrandymark0]
          stepcounterrandymark
          pgfcoordinaterandymarkarabicrandymarkpgfpoint0pt0pt
          %
          statestep[auto end on length=1.5pgfdecorationsegmentlength,
          auto corner on length=1.5pgfdecorationsegmentlength,
          width=+pgfdecorationsegmentlength]
          stepcounterrandymark%amplitudesetter
          pgfcoordinaterandymarkarabicrandymarkpgfpointpgfdecorationsegmentlengthrand*pgfdecorationsegmentamplitude
          %
          statefinal
          stepcounterrandymark
          pgfcoordinaterandymarkarabicrandymarkpgfpointdecoratedpathlast%
          %
          %

          pgfdeclaredecorationmark varying random y stepsstart
          %
          statestart[width=+0pt,next state=step,persistent precomputation=
          pgfdecoratepathhascornerstruesetcounterrandymark0]
          stepcounterrandymark
          pgfcoordinaterandymarkarabicrandymarkpgfpoint0pt0pt
          %
          statestep[auto end on length=1.5pgfdecorationsegmentlength,
          auto corner on length=1.5pgfdecorationsegmentlength,
          width=+pgfdecorationsegmentlength]
          stepcounterrandymark
          pgfmathsetmacromyfractionthepgfdecorationsegmentlength*valuerandymark/pgfdecoratedpathlength
          pgfmathsetmacromyamplitudevaryingamp(myfraction)
          %typeoutmyfraction,myamplitude
          pgfcoordinaterandymarkarabicrandymarkpgfpointpgfdecorationsegmentlengthrand*myamplitude*pgfdecorationsegmentamplitude
          %
          statefinal
          stepcounterrandymark
          pgfcoordinaterandymarkarabicrandymarkpgfpointdecoratedpathlast%
          %
          %



          begindocument
          begintikzpicture[x=5mm,y=5mm,decoration=mark random y steps,segment length=1.5mm,amplitude=0.75mm]% original curve
          draw[style=help lines] (0,-4) grid[step=5mm] (25,1);
          pgfmathsetseed2
          draw[blue!80!black,thick] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
          endtikzpicture

          vspace2ex

          begintikzpicture[x=5mm,y=5mm,decoration=mark varying random y steps,segment
          length=1.5mm,amplitude=0.75mm,declare function=
          varyingamp(x)=ifthenelse(x<0.08,1,ifthenelse(x<0.28,0,ifthenelse(x<0.48,5*(x-0.28),1)));]%
          draw[style=help lines] (0,-4) grid[step=5mm] (25,1);
          draw[red,thick] plot[variable=x,domain=0:25,samples=101] (x,varyingamp(x/25));
          pgfmathsetseed2
          draw[black] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
          path[decorate] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
          draw[blue!80!black,thick] plot[variable=x,samples at=1,...,arabicrandymark,smooth] (randymarkx);
          endtikzpicture

          vspace2ex

          begintikzpicture[x=2.5mm,y=2.5mm,decoration=mark varying random y
          steps,segment length=0.75mm,amplitude=0.75mm,declare function=
          varyingamp(x)=ifthenelse(x<0.08,1,ifthenelse(x<0.28,0,ifthenelse(x<0.48,5*(x-0.28),1)));]
          draw[style=help lines] (0,-4) grid[step=5mm] (25,1);
          pgfmathsetseed2
          draw[black] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
          path[decorate] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
          draw[blue!80!black,thick] plot[variable=x,samples at=1,...,arabicrandymark,smooth] (randymarkx);
          endtikzpicture
          enddocument


          enter image description here



          The function is shown in red in the second plot. The third plot shows scalability. (Of course, you also need to rescale the segment lengths. Notice also that this decoration has discrete steps, so if you have a strongly varying function but only a few steps, the function may not be fully "appreciated" since it only gets evaluated at a few points.)






          share|improve this answer













          Let me start by saying that I really like that question and am truly impressed by what you have achieved. Here is a proposal to address the scalability. Define a function that governs the amplitude,



          varyingamp(x) = whatever you like


          where x is the fraction of the decorated path (in order to ensure scalability). (Such a function has been used already here in order to have variable varying line widths. I would not at all be surprised if similar things had been used before.) This is the MWE.



          documentclassarticle
          usepackagetikz
          usetikzlibrarycalc,decorations.pathmorphing

          newcounterrandymark
          %newcommandamplitudesetter
          pgfdeclaredecorationmark random y stepsstart
          %
          statestart[width=+0pt,next state=step,persistent precomputation=
          pgfdecoratepathhascornerstruesetcounterrandymark0]
          stepcounterrandymark
          pgfcoordinaterandymarkarabicrandymarkpgfpoint0pt0pt
          %
          statestep[auto end on length=1.5pgfdecorationsegmentlength,
          auto corner on length=1.5pgfdecorationsegmentlength,
          width=+pgfdecorationsegmentlength]
          stepcounterrandymark%amplitudesetter
          pgfcoordinaterandymarkarabicrandymarkpgfpointpgfdecorationsegmentlengthrand*pgfdecorationsegmentamplitude
          %
          statefinal
          stepcounterrandymark
          pgfcoordinaterandymarkarabicrandymarkpgfpointdecoratedpathlast%
          %
          %

          pgfdeclaredecorationmark varying random y stepsstart
          %
          statestart[width=+0pt,next state=step,persistent precomputation=
          pgfdecoratepathhascornerstruesetcounterrandymark0]
          stepcounterrandymark
          pgfcoordinaterandymarkarabicrandymarkpgfpoint0pt0pt
          %
          statestep[auto end on length=1.5pgfdecorationsegmentlength,
          auto corner on length=1.5pgfdecorationsegmentlength,
          width=+pgfdecorationsegmentlength]
          stepcounterrandymark
          pgfmathsetmacromyfractionthepgfdecorationsegmentlength*valuerandymark/pgfdecoratedpathlength
          pgfmathsetmacromyamplitudevaryingamp(myfraction)
          %typeoutmyfraction,myamplitude
          pgfcoordinaterandymarkarabicrandymarkpgfpointpgfdecorationsegmentlengthrand*myamplitude*pgfdecorationsegmentamplitude
          %
          statefinal
          stepcounterrandymark
          pgfcoordinaterandymarkarabicrandymarkpgfpointdecoratedpathlast%
          %
          %



          begindocument
          begintikzpicture[x=5mm,y=5mm,decoration=mark random y steps,segment length=1.5mm,amplitude=0.75mm]% original curve
          draw[style=help lines] (0,-4) grid[step=5mm] (25,1);
          pgfmathsetseed2
          draw[blue!80!black,thick] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
          endtikzpicture

          vspace2ex

          begintikzpicture[x=5mm,y=5mm,decoration=mark varying random y steps,segment
          length=1.5mm,amplitude=0.75mm,declare function=
          varyingamp(x)=ifthenelse(x<0.08,1,ifthenelse(x<0.28,0,ifthenelse(x<0.48,5*(x-0.28),1)));]%
          draw[style=help lines] (0,-4) grid[step=5mm] (25,1);
          draw[red,thick] plot[variable=x,domain=0:25,samples=101] (x,varyingamp(x/25));
          pgfmathsetseed2
          draw[black] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
          path[decorate] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
          draw[blue!80!black,thick] plot[variable=x,samples at=1,...,arabicrandymark,smooth] (randymarkx);
          endtikzpicture

          vspace2ex

          begintikzpicture[x=2.5mm,y=2.5mm,decoration=mark varying random y
          steps,segment length=0.75mm,amplitude=0.75mm,declare function=
          varyingamp(x)=ifthenelse(x<0.08,1,ifthenelse(x<0.28,0,ifthenelse(x<0.48,5*(x-0.28),1)));]
          draw[style=help lines] (0,-4) grid[step=5mm] (25,1);
          pgfmathsetseed2
          draw[black] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
          path[decorate] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
          draw[blue!80!black,thick] plot[variable=x,samples at=1,...,arabicrandymark,smooth] (randymarkx);
          endtikzpicture
          enddocument


          enter image description here



          The function is shown in red in the second plot. The third plot shows scalability. (Of course, you also need to rescale the segment lengths. Notice also that this decoration has discrete steps, so if you have a strongly varying function but only a few steps, the function may not be fully "appreciated" since it only gets evaluated at a few points.)







          share|improve this answer












          share|improve this answer



          share|improve this answer










          answered Mar 17 at 16:02









          marmotmarmot

          118k6152286




          118k6152286







          • 1





            +1 for this amazing answer, and I wish I could +1 another time for the first sentence only...

            – JouleV
            Mar 17 at 16:03











          • @marmot you know you're driving me crazy, don't you? I did not even get a basic function implemented yet and you, well, uh. Ok, I'm digging through this one. Btw: x holds the fraction of pgfdecoratedpathlength, right? Even if your approach is more elegant than mine it's not the red curve that controls the amplitude... Therefore I would like to keep the question still open if you don't mind...

            – AndiW
            Mar 17 at 16:35






          • 1





            @AndiW Sorry for driving you crazy. ;-) The function drawn in red does determine the amplitude, i.e. the random deviation is rand*varyingamp(s)*pgfdecorationsegmentamplitude, where s denotes the fraction of the path we are at. Of course, s is not the x value of the curve at that point, which would not be independent of the coordinate system. You could of course define your own function that returns the path length s (or fraction) a a function of x, which would work in this specific case because here it is single-valued but in general it is not. (I'm just back from cycling.... )

            – marmot
            Mar 17 at 18:37






          • 1





            @AndiW Yes. What you are saying is correct, but is not contradicting with any of my statements, is it?

            – marmot
            Mar 17 at 20:21






          • 1





            @marmot well - actually I sometimes forget that LaTeX is no low-level-end-user tool. Given the fact that it's a function controling the amplitude and not a graph (which would be something an end-user would expect) the answer is great. Having quit physics 25 yrs ago I have to change my approach I guess... :-) +1!

            – AndiW
            Mar 17 at 21:04












          • 1





            +1 for this amazing answer, and I wish I could +1 another time for the first sentence only...

            – JouleV
            Mar 17 at 16:03











          • @marmot you know you're driving me crazy, don't you? I did not even get a basic function implemented yet and you, well, uh. Ok, I'm digging through this one. Btw: x holds the fraction of pgfdecoratedpathlength, right? Even if your approach is more elegant than mine it's not the red curve that controls the amplitude... Therefore I would like to keep the question still open if you don't mind...

            – AndiW
            Mar 17 at 16:35






          • 1





            @AndiW Sorry for driving you crazy. ;-) The function drawn in red does determine the amplitude, i.e. the random deviation is rand*varyingamp(s)*pgfdecorationsegmentamplitude, where s denotes the fraction of the path we are at. Of course, s is not the x value of the curve at that point, which would not be independent of the coordinate system. You could of course define your own function that returns the path length s (or fraction) a a function of x, which would work in this specific case because here it is single-valued but in general it is not. (I'm just back from cycling.... )

            – marmot
            Mar 17 at 18:37






          • 1





            @AndiW Yes. What you are saying is correct, but is not contradicting with any of my statements, is it?

            – marmot
            Mar 17 at 20:21






          • 1





            @marmot well - actually I sometimes forget that LaTeX is no low-level-end-user tool. Given the fact that it's a function controling the amplitude and not a graph (which would be something an end-user would expect) the answer is great. Having quit physics 25 yrs ago I have to change my approach I guess... :-) +1!

            – AndiW
            Mar 17 at 21:04







          1




          1





          +1 for this amazing answer, and I wish I could +1 another time for the first sentence only...

          – JouleV
          Mar 17 at 16:03





          +1 for this amazing answer, and I wish I could +1 another time for the first sentence only...

          – JouleV
          Mar 17 at 16:03













          @marmot you know you're driving me crazy, don't you? I did not even get a basic function implemented yet and you, well, uh. Ok, I'm digging through this one. Btw: x holds the fraction of pgfdecoratedpathlength, right? Even if your approach is more elegant than mine it's not the red curve that controls the amplitude... Therefore I would like to keep the question still open if you don't mind...

          – AndiW
          Mar 17 at 16:35





          @marmot you know you're driving me crazy, don't you? I did not even get a basic function implemented yet and you, well, uh. Ok, I'm digging through this one. Btw: x holds the fraction of pgfdecoratedpathlength, right? Even if your approach is more elegant than mine it's not the red curve that controls the amplitude... Therefore I would like to keep the question still open if you don't mind...

          – AndiW
          Mar 17 at 16:35




          1




          1





          @AndiW Sorry for driving you crazy. ;-) The function drawn in red does determine the amplitude, i.e. the random deviation is rand*varyingamp(s)*pgfdecorationsegmentamplitude, where s denotes the fraction of the path we are at. Of course, s is not the x value of the curve at that point, which would not be independent of the coordinate system. You could of course define your own function that returns the path length s (or fraction) a a function of x, which would work in this specific case because here it is single-valued but in general it is not. (I'm just back from cycling.... )

          – marmot
          Mar 17 at 18:37





          @AndiW Sorry for driving you crazy. ;-) The function drawn in red does determine the amplitude, i.e. the random deviation is rand*varyingamp(s)*pgfdecorationsegmentamplitude, where s denotes the fraction of the path we are at. Of course, s is not the x value of the curve at that point, which would not be independent of the coordinate system. You could of course define your own function that returns the path length s (or fraction) a a function of x, which would work in this specific case because here it is single-valued but in general it is not. (I'm just back from cycling.... )

          – marmot
          Mar 17 at 18:37




          1




          1





          @AndiW Yes. What you are saying is correct, but is not contradicting with any of my statements, is it?

          – marmot
          Mar 17 at 20:21





          @AndiW Yes. What you are saying is correct, but is not contradicting with any of my statements, is it?

          – marmot
          Mar 17 at 20:21




          1




          1





          @marmot well - actually I sometimes forget that LaTeX is no low-level-end-user tool. Given the fact that it's a function controling the amplitude and not a graph (which would be something an end-user would expect) the answer is great. Having quit physics 25 yrs ago I have to change my approach I guess... :-) +1!

          – AndiW
          Mar 17 at 21:04





          @marmot well - actually I sometimes forget that LaTeX is no low-level-end-user tool. Given the fact that it's a function controling the amplitude and not a graph (which would be something an end-user would expect) the answer is great. Having quit physics 25 yrs ago I have to change my approach I guess... :-) +1!

          – AndiW
          Mar 17 at 21:04

















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