circumsphere
Sam Sturgess
s.sturgess at minmet.uq.edu.au
Fri Mar 3 14:34:09 PST 2000
Hi
I got this email address from the follwing web page
http://www.ics.uci.edu/~eppstein/junkyard/circumcenter.html
I was looking for exactly what the question asks, ie
I am searching for a numerically stable algorithm to calculate the radius r
(and perhaps the center m) of the circumsphere of a tetrahedron in three
dimensions, given by the coordinates of the vertices a, b, c, d in R^3.
I am using the formula in a Delaunay Tessellation of a randomly packed bed
of spheres. Having worked through the formula given though I am confused,
as for a simple tetrahedron with vertex coordinates
a(0,0,00
b(0,1,0)
c(0,0,1)
d(1,0,0)
I found the centre to lie outside the tetrahedron at (0.5,0.5,0.5).
If you could explain this I'd greatly appreciate it. Otherwise if you know
of any references (such as a geometry text) that contains such a formula
and relevant explanations then I appreciate that as well.
Thank-you
Sam Sturgess (Masters Research)
Dept Mining Mineral Materials Engineering
University of Qld, Australia
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