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Approximate computation of curves on B-spline surfaces

yi-Jun yang 1, 2, 3 Song Cao 1, 2, 4 Jun-Hai yong 1, 2, 4 Hui Zhang 1, 2 Jean-Claude Paul 4, 1, 2 Jia-Guang Sun 1, 2, 3 He-Jin Gu 5 
4 CAD - Computer Aided Design
LIAMA - Laboratoire Franco-Chinois d'Informatique, d'Automatique et de Mathématiques Appliquées, Inria Paris-Rocquencourt
Abstract : Curves on surfaces play an important role in computer-aided geometric design. Because of the considerably high degree of exact curves on surfaces, approximation algorithms are preferred in CAD systems. To approximate the exact curve with a reasonably low degree curve which also lies completely on the B-spline surface, an algorithm is presented in this paper. The Hausdorff distance between the approximate curve and the exact curve is controlled under the user-specified distance tolerance. The approximate curve is ɛT –G1 continuous, where ɛT is the user-specified angle tolerance. Examples are given to show the performance of our algorithm.
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yi-Jun yang, Song Cao, Jun-Hai yong, Hui Zhang, Jean-Claude Paul, et al.. Approximate computation of curves on B-spline surfaces. Computer-Aided Design, Elsevier, 2008, 40 (2), pp.223-234. ⟨10.1016/j.cad.2007.10.011⟩. ⟨inria-00518325⟩

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