Parametric-surface adaptive tessellation based on degree reduction

Abstract

Parametric-surface tessellation is one of the most important algorithms for CAGD applications. This paper presents a new parametric-surface tessellation method based on degree reduction: (1) a given parametric surface (or NURBS surface) of degrees (p, q) is decomposed into a set of Bezier surfaces, (2) the Bezier surfaces are converted into a set of bilinear surfaces by applying consecutive stepwise degree reduction processes combined with adaptive subdivision-in each degree reduction step, a Bezier surface is adaptively subdivided until the approximation error from degree reduction is smaller than the corresponding step tolerance, (3) the bilinear surfaces are converted into a triangular net. The proposed method guarantees the resulting piecewise-planar approximant to deviate from the original parametric surface within a pre-defined tolerance, and to form a topologically water-tight triangular net. (C) 2002 Elsevier Science Ltd. All rights reserved.