POV-Ray : Newsgroups : povray.binaries.images : Circumscribed sphere : Re: Circumscribed sphere Server Time
3 May 2024 05:15:43 EDT (-0400)
  Re: Circumscribed sphere  
From: Bald Eagle
Date: 8 Aug 2014 11:35:01
Message: <web.53e4ed2c3cb258895e7df57c0@news.povray.org>
http://www.answers.com/topic/tetrahedron

"If OABC forms a general tetrahedron with a vertex O as the origin and vectors
a, b and c represent the positions of the vertices A, B, and C with respect to
O, then ... the radius of the circumsphere is given by:

R = |pow(a,2) * |bxc| + pow(b,2) * |cxa| + pow(c,2) |axb| | / 12V
where:
6V = |a.(bxc)|

Circumcenter O = |pow(a,2) * |bxc| + pow(b,2) * |cxa| + pow(c,2) |axb| | / 2a *
(bxc)

If I knew more about Delaunay triangulation or Voronoi cells, this might help me
out:
http://wias-berlin.de/software/tetgen/1.5/doc/manual/manual002.html
"In ℝ3, the vertices of the Voronoi diagram are the circumcenters of the
tetrahedra of the Delaunay tetrahedralization."


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