Approximate computation of curves on B-spline surfaces

Authors:
Yi-Jun Yang;Song Cao;Jun-Hai Yong;Hui Zhang;Jean-Claude Paul;Jia-Guang Sun;He-jin Gu
Affiliations:
School of Software, Tsinghua University, Beijing, China and Department of Computer Science and Tech., Tsinghua University, Beijing, China and Key Laboratory for Information System Security, Minist ...;School of Software, Tsinghua University, Beijing, China and Key Laboratory for Information System Security, Ministry of Education, China;School of Software, Tsinghua University, Beijing, China and Key Laboratory for Information System Security, Ministry of Education, China;School of Software, Tsinghua University, Beijing, China and Key Laboratory for Information System Security, Ministry of Education, China;School of Software, Tsinghua University, Beijing, China and Key Laboratory for Information System Security, Ministry of Education, China and INRIA, France;School of Software, Tsinghua University, Beijing, China and Department of Computer Science and Tech., Tsinghua University, Beijing, China and Key Laboratory for Information System Security, Minist ...;Jiangxi Academy of Sciences, Nanchang, China
Venue:
Computer-Aided Design
Year:
2008

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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 @e"T-G^1 continuous, where @e"T is the user-specified angle tolerance. Examples are given to show the performance of our algorithm.