Skip to main content

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


Comments

Post a Comment

Popular posts from this blog

plotting - How to draw lines between specified dots on ListPlot?

I would like to create a plot where I have unconnected dots and some connected. So far, I have figured out how to draw the dots. My code is the following: ListPlot[{{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4,13}, {2.5, 7}}, Ticks -> {{1, 2, 3, 4}, None}, AxesStyle -> Thin, TicksStyle -> Directive[Black, Bold, 12], Mesh -> Full] I have thought using ListLinePlot command, but I don't know how to specify to the command to draw only selected lines between the dots. Do have any suggestions/hints on how to do that? Thank you. Answer One possibility would be to use Epilog with Line : ListPlot[ {{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4, 13}, {2.5, 7}}, Ticks -> {{1, 2, 3, 4}, None}, AxesStyle -> Thin, TicksStyle -> Directive[Black, Bold, 12], Mesh -> Full, Epilog -> { Line[ ...
Post a Comment
Read more

equation solving - Invert and fit implicitly defined curve

I need to fit an implicitly defined curve. I thought I could get some data out of Solve , and then using FindFit . Therefore, I would like to find the relation the parametric curve defined by $F(x,y)=0$: Solve[-(1/2) + 1/2 (0.41202 BesselK[0, 0.1 Sqrt[x^2 + y^2]] + (0.101483 x BesselK[1, 0.1 Sqrt[x^2 + y^2]])/Sqrt[x^2 + y^2]) == 0, y] But I can't get an output: Solve was unable to solve the system with inexact coefficients or the system obtained by direct rationalization of inexact numbers present in the system. Since many of the methods used by Solve require exact input, providing Solve with an exact version of the system may help. >> Edit: In particular, I would like to fit the data coming from the curve with the expression of another curve, and not with a function $f(x)$. In particular, since this clearly looks like a cardioid , I would like it to fit to something like it. What other strategies could I try?
Post a Comment
Read more

dynamic - How can I make a clickable ArrayPlot that returns input?

I would like to create a dynamic ArrayPlot so that the rectangles, when clicked, provide the input. Can I use ArrayPlot for this? Or is there something else I should have to use? Answer ArrayPlot is much more than just a simple array like Grid : it represents a ranged 2D dataset, and its visualization can be finetuned by options like DataReversed and DataRange . These features make it quite complicated to reproduce the same layout and order with Grid . Here I offer AnnotatedArrayPlot which comes in handy when your dataset is more than just a flat 2D array. The dynamic interface allows highlighting individual cells and possibly interacting with them. AnnotatedArrayPlot works the same way as ArrayPlot and accepts the same options plus Enabled , HighlightCoordinates , HighlightStyle and HighlightElementFunction . data = {{Missing["HasSomeMoreData"], GrayLevel[ 1], {RGBColor[0, 1, 1], RGBColor[0, 0, 1], GrayLevel[1]}, RGBColor[0, 1, 0]}, {GrayLevel[0], GrayLevel...
Post a Comment
Read more