Calculating Frenet triples in mathematica

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aguacate
Posts: 209
Joined: Fri Feb 16, 2007 10:29 pm UTC

Calculating Frenet triples in mathematica

Postby aguacate » Thu Jan 24, 2008 2:12 am UTC

Does anyone know if mathematica can calculate the curvature and torsion of a vector function? I would like to double check my geometry homework.
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acidhak
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Joined: Sat Jan 26, 2008 6:15 pm UTC

Re: Calculating Frenet triples in mathematica

Postby acidhak » Sat Jan 26, 2008 7:05 pm UTC

I believe that this would require you to write modules first, i.e. there is no command to do this. If its for one time use, just compute from the definitions as things like gradient, dot product, cross product and norm are all very straight forward to use.

Here's one I had lying around for Gaussian curvature but I don't know if that helps you or not:

gaussK[x_][u_,v_] := Module[{xu,xv,xuu,xuv,xvv},

xu=D[x[uu,vv],uu]; xv=D[x[uu,vv],vv];

xuu=D[x[uu,vv],uu,uu];

xuv=D[x[uu,vv],uu,vv];

xvv=D[x[uu,vv],vv,vv];

Simplify[(Det[{xuu,xu,xv}]*Det[{xvv,xu,xv}]-Det[{xuv,xu,xv}]^2)/

(xu.xu*xv.xv-(xu.xv)^2)^2]]/.{uu->u,vv->v}

make it a .m file...

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NathanielJ
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Joined: Sun Jan 13, 2008 9:04 pm UTC

Re: Calculating Frenet triples in mathematica

Postby NathanielJ » Wed Jan 30, 2008 3:35 am UTC

I can't seem to find a pre-written mathematica module for things like torsion and curvature, but if you're able to use Maple instead then there are dozens of functions floating around the internet that will do it for you (even just a quick Google search pops up tons of them).
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