ON VANISHING NORMAL OF TENSOR PRODUCT SURFACES

摘要

Vanishing normal of tensor product surfaces is an unwanted phenomenon (a kind of singularity) that designers want to avoid. We move one control point while the rest is fixed, and specify those positions of the moving control point that results in a vanishing normal at an arbitrarily specified point of the surface. We show that this locus is a straight line. Beside the generic case, we examine Bezier surfaces in more detail, since Bernstein polynomials facilitate the simplification of formulae.