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Groups > comp.lang.postscript > #2497
| From | Scott Hemphill <hemphill@hemphills.net> |
|---|---|
| Newsgroups | comp.lang.postscript |
| Subject | Re: How long is a path? Alas currentdash is silent |
| References | <7d687ea2-4b38-408d-be5f-e35d730137eb@googlegroups.com> <1regqufm4mopi$.y2znd2xxsk3k$.dlg@40tude.net> <c29bc460-0e9e-44ef-a259-9df1a6e33bac@googlegroups.com> <7f3d04a0-d6c3-4665-bae3-142f0c149284@googlegroups.com> <c50435f5-05ba-4793-b557-55dff3575a5e@googlegroups.com> |
| Date | 2016-04-06 11:40 -0400 |
| Message-ID | <87y48qkanw.fsf@hemphills.net> (permalink) |
jdaw1 <jdawiseman@gmail.com> writes:
> And in case it wasn't obvious, the length of a curve has to be
> approximated numerically as it doesn't integrate analytically. :-(
>
> Mathematica:
>
>
> KnotsFromCoeffs[{c0_, c1_, c2_, c3_}] = {c0, c0 + c1/3, c0 + (2 c1 +
> c2)/3, c0 + c1 + c2 + c3};
> CoeffsFromKnots[{z0_, z1_, z2_, z3_}] = {z0, -3 z0 + 3 z1, 3 z0 - 6 z1
> + 3 z2, -z0 + 3 z1 - 3 z2 + z3};
>
> x = Table[t^i, {i, 0, 3}].CoeffsFromKnots[{x0, x1, x2, x3}];
> y = Table[t^i, {i, 0, 3}].CoeffsFromKnots[{y0, y1, y2, y3}];
>
> lengthPiece = Sqrt[Collect[D[x, t]^2 + D[y, t]^2, t]] // Simplify;
> Print[lengthPiece];
> length = Integrate[lengthPiece, {t, 0, 1}];
> Print[length];
Did you let the integration complete? In my case, I just integrated
Sqrt[a + b*t + c*t^2 + d*t^3 + e*t^4]
You get an answer in terms of square roots, trig functions, elliptic
integrals, and roots of the quartic. But the roots of the quartic are
analytical. So I'd say that it does integrate analytically. However, it
is so messy, I'd rather approximate it numerically.
Scott
--
Scott Hemphill hemphill@alumni.caltech.edu
"This isn't flying. This is falling, with style." -- Buzz Lightyear
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How long is a path? Alas currentdash is silent jdaw1 <jdawiseman@gmail.com> - 2016-04-05 16:34 -0700
Re: How long is a path? Alas currentdash is silent tlvp <mPiOsUcB.EtLlLvEp@att.net> - 2016-04-05 21:45 -0400
Re: How long is a path? Alas currentdash is silent luser- -droog <mijoryx@yahoo.com> - 2016-04-05 19:09 -0700
Re: How long is a path? Alas currentdash is silent jdaw1 <jdawiseman@gmail.com> - 2016-04-06 01:26 -0700
Re: How long is a path? Alas currentdash is silent jdaw1 <jdawiseman@gmail.com> - 2016-04-06 05:07 -0700
Re: How long is a path? Alas currentdash is silent Scott Hemphill <hemphill@hemphills.net> - 2016-04-06 11:40 -0400
Re: How long is a path? Alas currentdash is silent jdaw1 <jdawiseman@gmail.com> - 2016-04-06 09:52 -0700
Re: How long is a path? Alas currentdash is silent sjprouty3765@gmail.com - 2016-04-06 12:05 -0700
Re: How long is a path? Alas currentdash is silent jdaw1 <jdawiseman@gmail.com> - 2016-04-06 14:55 -0700
Re: How long is a path? Alas currentdash is silent Scott Hemphill <hemphill@hemphills.net> - 2016-04-06 17:12 -0400
Re: How long is a path? Alas currentdash is silent jdaw1 <jdawiseman@gmail.com> - 2016-04-06 14:34 -0700
Re: How long is a path? Alas currentdash is silent Scott Hemphill <hemphill@hemphills.net> - 2016-04-06 11:35 -0400
Re: How long is a path? Alas currentdash is silent jdaw1 <jdawiseman@gmail.com> - 2016-04-06 09:38 -0700
Re: How long is a path? Alas currentdash is silent jdaw1 <jdawiseman@gmail.com> - 2016-04-07 01:39 -0700
Re: How long is a path? Alas currentdash is silent Carlos <angus@quovadis.com.ar> - 2016-04-08 15:04 +0200
Re: How long is a path? Alas currentdash is silent jdaw1 <jdawiseman@gmail.com> - 2016-04-08 14:32 -0700
Re: How long is a path? Alas currentdash is silent Carlos <angus@quovadis.com.ar> - 2016-04-09 01:19 +0200
Re: How long is a path? Alas currentdash is silent jdaw1 <jdawiseman@gmail.com> - 2016-04-08 14:57 -0700
Re: How long is a path? Alas currentdash is silent Carlos <angus@quovadis.com.ar> - 2016-04-09 01:31 +0200
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