Curvature of singular Bézier curves and surfaces

Authors:
Thomas W. Sederberg;Hongwei Lin;Xin Li
Affiliations:
Department of Computer Science, Brigham Young University, Provo, UT 84602, USA;State Key Lab of CAD&CG, Zhejiang University, Hangzhou 310058, China;Department of Mathematics, University of Science and Technology of China, Hefei, China
Venue:
Computer Aided Geometric Design
Year:
2011

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Abstract

This paper presents a general approach for finding the limit curvature at a singular endpoint of a rational Bezier curve and the singular corner of a rational Bezier surface patch. Conditions for finite Gaussian and mean limit curvatures are expressed in terms of the rank of a matrix.