Bezier Crust on Quad Subdivision Surface

Abstract

Subdivision surfaces have been widely used in computer graphics and can be classified into two categories, approximating and interpolatory. Representative approximating schemes are Catmull-Clark (quad) and Loop (triangular). Although widely used, one issue remains with the approximating schemes, i.e., the process of interpolating a set of data points is a global process so it is difficult to interpolate large data sets. In this paper, we present a local interpolation scheme for quad subdivision surfaces through appending a G2 Bezier crust to the underlying surface, and show that this local interpolation scheme does not change the curvatures across the boundaries of underlying subdivision patches, therefore, one obtains high quality interpolating limit surfaces for engineering and graphics applications efficiently.