Journal for Geometry and Graphics, Vol. 5, No. 2, pp. 145-155 (2001)

A Basic Evaluation Method of Subdivision Surfaces

Yasushi Yamaguchi

Department of Graphics and Computer Sciences, Graduate School
of Arts and Sciences, The University of Tokyo
3-8-1 Komaba, Meguro-ku, Tokyo 153-8902, Japan

Abstract: A subdivision surface is a powerful tool to represent a smooth surface with arbitrary topology. It starts with a control polyhedron which roughly approximates the final surface. The polyhedron gradually approaches to the final surface by subdividing faces more closely to approximate the final surface. However, it is not so popular in engineering applications because of the procedural nature. Algorithms for parametric surfaces cannot be applicable to a procedural surface. This paper discusses a method for evaluating a subdivision surface with parametric values based on Stam's work. Our approach gained stability around an extraordinary point as well as the convergence of a normal vector at the point.

Keywords: Subdivision surface, Catmull-Clark surface, Loop surface

Classification (MSC2000): 68U05; 53A05

Full text of the article will be available in mid of 2003.

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