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Re: Re: Text on a curve

• To: mathgroup at smc.vnet.net
• Subject: [mg104783] Re: [mg104767] Re: [mg104758] Text on a curve
• From: DrMajorBob <btreat1 at austin.rr.com>
• Date: Tue, 10 Nov 2009 05:57:20 -0500 (EST)
• References: <12231782.1257682834657.JavaMail.root@n11>
• Reply-to: drmajorbob at yahoo.com

For those who, like myself, might have searched for the "Text on a curve"  
solution at the links below...

It is already posted at the first link, at the bottom of the page. Posts  
go from oldest to newest, it appears. I expected the opposite (oddly  
enough), so I initially thought the solution hadn't been posted yet.

The examples are individually amazing, and as a group they cover many of  
the hardest graphics issues we're likely to encounter. Even if you don't  
have Presentations, they illustrate a lot of useful mathematics on curves  
and surfaces.

(On a less helpful note... I found no clue where David's solutions might  
be found at the second link.)

Bobby

On Mon, 09 Nov 2009 04:44:59 -0600, David Park <djmpark at comcast.net> wrote:

> Here is a solution using the Presentations package. A fuller solution  
> with
> more detailed explanation should appear in a few days on Peter Linday's
> site:
>
> http://blackbook.mcs.st-and.ac.uk/~Peter/djmpark/html/
>
> at the University of St Andrews School of Mathematics and Statistics:
>
> http://www.mcs.st-and.ac.uk/
>
> There are both Mathematica notebooks and PDF files there for solutions to
> various MathGroup questions.
>
> To put text around a curve it is probably best to use a unit speed
> parametrization for the curve, to use a mono-space character font, and to
> confine the text to portions of the curve where it will read right side  
> up
> and left to right. For those who have Presentations, here is a solution:
>
> Needs["Presentations`Master`"]
>
> curve[t_] := {Cos[t] + Sin[t], Sin[t]}
> v[t_] = Simplify[Norm[curve'[t]], t \[Element] Reals]
> curvelength = NIntegrate[v[t], {t, 0, 2 \[Pi]}]
>
> ClearAll[t];
> First@NDSolve[{t'[s] == 1/v[t[s]], t[0] == 0}, t, {s, 0, curvelength}];
> t[s_] = t[s] /. %
>
> unitspeed[s_] = curve[t[s]]
>
> Module[
>  {string = "We were asked to wrap some text around a curve.",
>   characters, numchar, point, tangent, normal, txt},
>  characters = Characters[string];
>  numchar = Length[characters];
>  (* Define the position, tangent and normal for character i *)
>  point[i_] := unitspeed[Rescale[i, {1, numchar}, {5.0, 0.5}]];
>  tangent[i_] := unitspeed'[Rescale[i, {1, numchar}, {5.0, 0.5}]];
>  normal[i_] := Normalize[Reverse[tangent[i]] {-1, 1}];
> Draw2D[
>   {{Blue, Thick, ParametricDraw[unitspeed[s], {s, 0, curvelength}]},
>    Table[
>     (* Character at its position along the curve *)
>     txt =
>      Text[Style[characters[[i]], 14, Bold, FontFamily -> "Courier"],
>       point[i]];
>     (* Rotate so the character baseline is along the tangent *)
>     txt = txt // RotationTransformOp[{{1, 0}, -tangent[i]}, point[i]];
>     (* Translate a fixed distance along the normal away from the \
> curve *)
>     txt // TranslateOp[-.1 normal[i]], {i, 1, numchar}]},
>   Frame -> True,
>   PlotRangePadding -> .2,
>   ImageSize -> 300]
>  ]
>
>
> David Park
> djmpark at comcast.net
> http://home.comcast.net/~djmpark/
>
>
>
>
> From: Bill [mailto:WDWNORWALK at aol.com]
>
> 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
>
>
>


-- 
DrMajorBob at yahoo.com