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Re: Text on a curve

  • To: mathgroup at smc.vnet.net
  • Subject: [mg104794] Re: Text on a curve
  • From: dh <dh at metrohm.com>
  • Date: Tue, 10 Nov 2009 05:59:24 -0500 (EST)
  • References: <hd6bh0$olc$1@smc.vnet.net>


Bill wrote:

> Text on a curve

> 

> 

> Hi:

> 

> Using the following Mathematica 6.0.1 code, I get a nice picture as follows:

> 

> Module[{f, fs, t}, f[t_] = {Cos[t] + Sin[t], Sin[t]};

>  fs[t_] = D[f[t], t] // N;

>  h = Graphics[Rotate[Style[Text["

>       T"], 14], 90 Degree]];

>  Show[Graphics[{Arrowheads[{{Automatic, Automatic, h}}], {Red, 

>        Arrow /@ 

>         MapThread[{#1 + 

>             0.001 #2, (#1 - 

>              2 #2)} &, {f /@ #, ({-1, 1} Reverse[#]/21) & /@ (#/

>                  Sqrt[#.#] & /@ (fs /@ #))} &[#]]}, {Thickness[0.005], {Blue, 

>         Line[f /@ #]}}} &[

>     Table[\[Rho], {\[Rho], 0.0, 2*Pi // N, 2*Pi/26 // N}]]], 

>   AspectRatio -> Automatic, Axes -> True, 

>   PlotRange -> {{-1.6, 1.6}, {-1.6, 1.6}}, ImageSize -> 500]]

>   

>   Question: How can the code be modified to place selected letters at different positions, forming a sentence around the curve, such as:

>   

>   ~Typing onto a curve

>   

>   

>   

>   Thanks,

>   

>   Bill

> 

Hi Bill,

you need to declare a different arrowhead for each arrow. E.g.:



Module[{f, fs, t}, f[t_] = {Cos[t] + Sin[t], Sin[t]};

  fs[t_] = D[f[t], t] // N;



  h = Graphics[

      Rotate[Style[Text["\n" <> #], {0, 100}, 14], 90 Degree]] & /@

    Characters["Typing onto a curve works   "];

  i = 0;

  Show[Graphics[{{Red, {Arrowheads[{{Automatic, Automatic, h[[++i]]}}],

            Arrow[#]} & /@

         MapThread[{#1 +

             0.001 #2, (#1 -

              2 #2)} &, {f /@ #, ({-1, 1} Reverse[#]/21) & /@ (#/

                  Sqrt[#.#] & /@ (fs /@ #))} &[#]]}, {Thickness[

         0.005], {Blue, Line[f /@ #]}}} &[

     Table[\[Rho], {\[Rho], 0.0, 2*Pi // N, 2*Pi/26 // N}]]],

   AspectRatio -> Automatic, Axes -> True,

   PlotRange -> {{-1.6, 1.6}, {-1.6, 1.6}}, ImageSize -> 500]]





Daniel




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