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MathGroup Archive 1998

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RE:[mg 14178]Re: Very slow graphics rendering

  • To: mathgroup at smc.vnet.net
  • Subject: [mg14187] RE:[mg 14178]Re: Very slow graphics rendering
  • From: "Julio Vera" <lvera at varela.reu.edu.uy>
  • Date: Wed, 30 Sep 1998 19:42:20 -0400
  • Sender: owner-wri-mathgroup at wolfram.com

Thanks very much to Paul Abbott. The polar expression seems to solve the
problem quite well. It is much faster.

It looks like the thing is to "draw" the curve in the same direction as
the limit curve will be. Thus, the polar writing of the sphere goes by
circles that are paralell to the x plane.

I am trying to figure out if this is applicable to curve limits that are
not paralell to one of the axes plane. Like the intersection of the
same sphere with this plane

z=1-x+y

Or with curve limits that are not circles or straight lines, like the
intersection of the former plane with this cone

((1+z)/2)^2=x^2+y^2


> However, an alternative (polar) parameterization might be better:
> 
> ParametricPlot3D[{r*Cos[t], r*Sin[t], 
>     If[r < 4/5, Sqrt[1 - r^2], Sqrt[1 - (4/5)^2]]}, 
> 		{r, 0, 4/5}, {t, 0, 2*Pi}]; 

Thank you for your help and your time.

Julio Vera


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