Rational quadratic Bezier triangles on quadrics

Abstract

First, different ways of solving the problem, if a given rational triangular Bezier patch of degree 2 lies on a quadric surface, are presented. Although these approaches are theoretically equivalent, their difference from the practical point of view is illustrated by analysing and comparing the numerical condition of the respective problems. Second, given a rational triangular Bezier patch of degree 2 in standard form with five fixed control points, geometrical conditions on the locus of the sixth control point are derived and the remaining inner weights are determined. The locus of this remaining control point results to be part of a quadric surface. The obtained results are illustrated for a representative example.