Re: Ray Trace

*To*: mathgroup at smc.vnet.net*Subject*: [mg33601] Re: Ray Trace*From*: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>*Date*: Wed, 3 Apr 2002 01:13:25 -0500 (EST)*Organization*: Universitaet Leipzig*References*: <a81juj$783$1@smc.vnet.net>*Reply-to*: kuska at informatik.uni-leipzig.de*Sender*: owner-wri-mathgroup at wolfram.com

Hi, a) what is a *flat* polygon surface ? Do you mean a polygonal approximation to a surface ? b) a polygonal approximation to a surface uses *triangles* not quadrangles otherwise the surface between the points is not a polygon c) say your points are {px[1],py[1],py[1]},{px[2],py[2],py[2]}, .. with these four points you can make a parametric patch { a[1]+b[1]*u+c[1]*v+d[1]*u*v, a[2]+b[2]*u+c[2]*v+d[2]*u*v, a[3]+b[3]*u+c[3]*v+d[3]*u*v} with u, v in [0,1] this can be solved by Mathematica and you have your parametric representation of the surface patch. For a[1],b[1],c[1],d[1] one gets {a[1] -> px[1], b[1] -> -px[1] + px[2], c[1] -> -px[1] + px[3], d[1] -> px[1] - px[2] - px[3] + px[4]} Such approximation is not smooth on the polygon edges. That's why spline surfaces are constructed, but a spline surface need more than four points d) for a curved surface you need the two principal curvatures and the corresponding directions. Regards Jens Regards Jens Shawn O'Connor wrote: > > flat polygon surfaces are relatively simple to define and use. I would like > specify a curved rectangular duct with a certain curvature. Is there an > easy way to define a curved surface given four points that pass through it? > Then check weather a point lies on that plane bounded by the points. I can > do this already for flat surfaces. > > Thank you