Geometric continuity between adjacent Bézier patches and their constructions

Authors:
Xiuzi Ye;Youdong Liang;Horst Nowacki
Affiliations:
Institut für Schiffs- und Meerestechnik, Technische Universität Berlin, Sekr. SG 10, Satzufer 17-19, 10587 Berlin, Germany;State Key Laboratory of CAD/CG and Department of Applied Mathematics, Zhejiang University, 310013 Hangzhou, P. R. China;Institut für Schiffs- und Meerestechnik, Technische Universität Berlin, Sekr. SG 10, Satzufer 17-19, 10587 Berlin, Germany
Venue:
Computer Aided Geometric Design
Year:
1996

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Abstract

In this paper, the necessary and sufficient conditions for two adjacent Bezier surface patches of arbitrary degrees joining G^n-continuously along a common boundary curve are presented. These conditions are represented directly by the two surface patches, or via an intermediate surface patch. Configurations of the coefficient functions attached to the adjacent Bezier patches are obtained. Based on these results, an algorithm to compute the order of continuity between two given Bezier patches along a common boundary curve is presented. The G^n compatibility conditions which involve the coefficient functions and the control points of the two adjacent Bezier patches are developed. Examples for the construction of G^1- and G^2-continuous Bezier patches are given to illustrate the conditions developed.