AN IMPLEMENTATION OF TRIANGULAR B-SPLINE SURFACES OVER ARBITRARY TRIANGULATIONS

A new multivariate B-spline scheme based on blending functions and control vertices has recently been developed by Dahmen, Micchelli, and Seidel (1992). This surface scheme allows us to model piecewise polynomial surfaces of degree k over arbitrary triangulations, such that the resulting surfaces are C(k-1)-continuous everywhere. The scheme exhibits both affine invariance and the convex hull property, and the control points can be used to manipulate the shape of the surface locally. Any piecewise polynomial can be represented by the new scheme [Seidel '92]. This paper illustrates some of the algorithms underlying the new scheme by means of examples from a first test implementation [Fong '92].