Computer & Graphics '02
Parametric surface tessellation based on degree reduction
Byoung K. Choi
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.
Keywords: Parametric-surface tessellation; stepwise degree reduction; adaptive subdivision; piecewise-planar approximant; water-tight triangular net