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graphics - Movable text on a curve


Having an arbitrary curve defined as InterpolatingFunction, what is the best way to place a text on this curve? The text generally has two rows, for example: "This is\na text on a curve", the curve must go between the rows. I am interested both in character-based (preserving characters as selectable textual elements) and outlined solution (the text is first converted to outlines, then a transformation is applied to the resulting curves). It would be perfect to have a possibility to move the text along the curve interactively.


External links (updated!):




  1. Warping Text to a Bézier curves (Jay's Projects)





  2. Geometric shaping of a text (Wolfram Community)





For the search engine: this is also known as "text on a path."



Answer



Here's another way...Text[] has a direction argument, so ArcTan is not necessary.


txt1 = "Now we can follow" // Characters;
txt2 = "an arbitrary path" // Characters;
f[t_] := {Cos[2 π t], Sin[6 π t]};

totalarclength = NIntegrate[Sqrt[f'[Ï„].f'[Ï„]], {Ï„, 0, 1}];
invarclength = First@NDSolve[{D[$t[s], s] == 1/Sqrt[f'[$t[s]].f'[$t[s]]], $t[0] == 0},
$t, {s, 0, totalarclength}];
ds = 0.12;
fs = Scaled[0.08];

Manipulate[
  Show[
    ParametricPlot[f[t], {t, 0, 1}],
    Graphics[{

      Table[Text[Style[txt1[[n]], "Text", FontSize -> fs],
        f[$t[Mod[s0 + n ds, totalarclength]] /. invarclength],
        {0, -1.1},
        f'[$t[Mod[s0 + n ds, totalarclength]] /. invarclength]],
        {n, Length[txt1]}], 
      Table[Text[Style[txt2[[n]], "Text", FontSize -> fs],
        f[$t[Mod[s0 + n ds, totalarclength]] /. invarclength],
        {0, 1.1},
        f'[$t[Mod[s0 + n ds, totalarclength]] /. invarclength]],
        {n, Length[txt2]}]}],

    PlotRangePadding -> Scaled[0.09]
  ],
  {s0, 0, totalarclength}
]

Computing the arclength can help space the characters out. As far as I know, Mathematica does not provide access to character widths, so that equal spacing is probably as good as one can do easily. As someone has remarked, tight curvatures pose a problem.


Mathematica graphics


Addendum


One of Alexey Popkov's comments suggested the following modification, with help from the FilledCurve doc page. The glyphs are distorted by the curvature, and tight curvatures cause inversion.


txtbase = ImportString[ExportString["some movable text", "PDF"], "PDF"];

txt = First@First@txtbase;
xRange = -Subtract @@ First[PlotRange /. First@AbsoluteOptions[txtbase, PlotRange]];
c[t_] := {Cos[2 π t], Sin[6 π t]};
totalarclength = NIntegrate[Sqrt[c'[Ï„].c'[Ï„]], {Ï„, 0, 1}];
invarclength = First@NDSolve[{D[$t[s], s] == 1/Sqrt[c'[$t[s]].c'[$t[s]]], $t[0] == 0},
$t, {s, 0, totalarclength}];
NN[t_] := {{0, -1}, {1, 0}}.c'[t]/Sqrt[c'[t].c'[t]];
maptext[s_, Δn_] := With[{t = $t[Mod[s, totalarclength]] /. invarclength}, 
  c[t] + Δn NN[t]];
Manipulate[

  Show[
    ParametricPlot[c[t], {t, 0, 1}],
    Graphics[
      Dynamic@{txt /. {x_Real, y_Real} :> maptext[-fs x/xRange + s0, -fs y/xRange + ΔN]}],
    PlotRange -> 1.5
  ],
  {{ΔN, 0.1}, -1, 1},
  {{s0, 6.45}, 0, totalarclength},
  {{fs, 2, "font scale"}, 0.1, 5}
]


Mathematica graphics


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