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Conway on Trilinear vs Barycentric
Posted:
Jul 1, 1998 10:34 PM
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I read all of this and still can't fathom which of
these coordinate system types is this:
(0,0,1)
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/ \
/ \
/ \
(1,0,0) (0,1,0)
Any point P is reachable by linear combination of
basis vectors. Only positive scalars required
(vector reversal operation not required to span
plane, only grow/shrink and tip-to-tail addition).
The 4 basis vector analog of the above is what
I've dubbed "quadrays" and describe at my website
at http://www.teleport.com/~pdx4d/quadrays.html
-- 4 vectors from the origin thru the vertices
of a regular tetrahedral enclosure. All points
in volume uniquely identified by 4-tuples with
no negative scalars.[1]
Kirby
[1] we can define negative scalars and include
vector reversal i.e. multiplication of a vector
by -1, but these more provide redundant shortcuts
in notation than trully novel operations.
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