QUASI-HARMONIC CONSTRAINTS FOR TORIC BEZIER SURFACES

Abstract

Toric Bezier patches generalize the classical tensor-product triangular and rectangular Bezier surfaces, extensively used in CAGD. The construction of toric Bezier surfaces corresponding to multi-sided convex hulls for known boundary mass-points with integer coordinates (in particular for trapezoidal and hexagonal convex hulls) is given. For these toric Bezier surfaces, we find approximate minimal surfaces obtained by extremizing the quasi-harmonic energy functional. We call these approximate minimal surfaces as the quasi-harmonic toric Bezier surfaces. This is achieved by imposing the vanishing condition of gradient of the quasi-harmonic functional and obtaining a set of linear constraints on the unknown inner mass-points of the toric Bezier patch for the above mentioned convex hull domains, under which they are quasi-harmonic toric Bezier patches. This gives us the solution of the Plateau toric Bezier problem for these illustrative instances for known convex hull domains.