G1 continuous approximate curves on NURBS surfaces

Authors:
Yi-Jun Yang;Wei Zeng;Cheng-Lei Yang;Xiang-Xu Meng;Jun-Hai Yong;Bailin Deng
Affiliations:
School of Computer Science and Tech., Shandong Univ., Jinan, China;Computer Science Department, State Univ. of New York at Stony Brook, USA;School of Computer Science and Tech., Shandong Univ., Jinan, China;School of Computer Science and Tech., Shandong Univ., Jinan, China;School of Software, Tsinghua Univ., Beijing, China;Computer Graphics and Geometry Laboratory, EPFL, Switzerland
Venue:
Computer-Aided Design
Year:
2012

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Abstract

Curves on surfaces play an important role in computer aided geometric design. In this paper, we present a parabola approximation method based on the cubic reparameterization of rational Bezier surfaces, which generates G^1 continuous approximate curves lying completely on the surfaces by using iso-parameter curves of the reparameterized surfaces. The Hausdorff distance between the approximate curve and the exact curve is controlled under the user-specified tolerance. Examples are given to show the performance of our algorithm.