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Quadray coordinates
Quadray coordinates, also known as tetray coordinates or Chakovian coordinates, were Invented by Darrel Jarmusch and further developed by David Chako, Tom Ace, Kirby Urner, et al., as another take on simplicial coordinates, a coordinate system using the simplex or tetrahedron as its basis polyhedron.〔Urner, Kirby. "Teaching Object-Oriented Programming with Visual FoxPro." ''FoxPro Advisor'' (Advisor Media, March, 1999), page 48 ff.〕
==Geometric definition==
The four basis vectors stem from the origin of the regular tetrahedron and go to its four corners. Their coordinate addresses are (1, 0, 0, 0), (0, 1, 0, 0), (0, 0, 1, 0) and (0, 0, 0, 1) respectively. These may be scaled and linearly combined to span conventional ''XYZ'' space, with at least one of the four coordinates unneeded (set to zero) in any given quadrant.
The normalization scheme is somewhat unusual in keeping all coordinates non-negative. Typical of coordinate systems of this type (a, a, a, a) is an identity vector and may be added to normalize a result. To negate (1,0,0,0), write (−1, 0, 0, 0) then add (1, 1, 1, 1) to get (0, 1, 1, 1).
Four basis quadrays to the corners of a regular tetrahedron
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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