circumsphere

[Sam Sturgess]

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


-------------
The compgeom mailing lists: see
http://netlib.bell-labs.com/netlib/compgeom/readme.html
or send mail to compgeom-request at research.bell-labs.com with the line:
send readme
Now archived at http://uiuc.edu/~sariel/CG/compgeom/maillist.html.