Convex Sets, Barycentric Coordinates, Triangulations, and Ambiguity:
(April 6, 2002)

Why do barycentric coordinates fail to provide unique values for more than N control points (in an N-dimensional space)? (use elevation/height map interpretation, and relate this to tessellation ambiguity).

Give useful applications to interpolation between arbitrary number of points in Rⁿ. Then explain spanning sets, simplices, why we want to project onto minimal basis, etc.