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