December 21 2016

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In this post I want to present an easy method to obtain a discrete parametrization of a surface S defined implicitly (f(x,y,z)=0).

This problem was discussed here several times, the most recent post is

http://www.mapleprimes.com/posts/207661-Isolation-Of-Sides-Of-The-Surface-On-The-Graph

S is supposed to be the boundary of a convex body having (x0,y0,z0) an interior point and contained in a ball of radius R centered at (x0,y0,z0).

Actually, the procedure also works if the body is only star-shaped with respect to the interior point, and it is also possible to plot only a part of the surface

inside a solid angle centered at (x0,y0,z0).

*Usage:*

Par3d(f, x=x0, y=y0, z=z0, R, m, n, theta1 .. theta2, phi1 .. phi2)

f