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Topic: Conway on Trilinear vs Barycentric coordinates
Replies: 13   Last Post: Feb 16, 1999 8:05 AM

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Posts: 6
Registered: 12/8/04
Re: Article on Quadrays in March 1999 FoxPro Advisor
Posted: Feb 7, 1999 8:06 AM
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The permutations of quadray (2,1,1,0) are similar to my system. Subtract one
from each coordinate and you get (1,0,0,-1) and the twelve unique permutations
are the vertices of a cuboctahedron in my system. But the permutations of
(1,0,0,0) in quadrays are not the centers of closest packed spheres. They are
something that requires fractions in my system. The idea is to use integers
(mod a prime), and get only the centers of closest packed spheres.

By the way, is arithmetic remainder (as well as modulo) a prime a field?

Bucky wrote that the tetrahedron's four dimensions refer to the distances from
the midpoint of the tetrahedron to the centers of the four faces. The
advantage of that is to represent any size (positive or negative) tetrahedron
anywhere with four coordinates. There is a way to transform from my system to
quadrays just as there is a way to transform to XYZ. (or if the four
coordinates do not sum to zero, to XYZT).

Cliff Nelson
<A HREF="http://forum.swarthmore.edu/epigone/geometry-research/brydilyum">RBF
electronic notebooks by Clifford J. Nelson

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