Algorithm for orthogonal projection of parametric curves onto B-spline surfaces

Authors:
Hai-Chuan Song;Jun-Hai Yong;Yi-Jun Yang;Xiao-Ming Liu
Affiliations:
School of Software, Tsinghua University, Beijing 100084, PR China and Key Laboratory for Information System Security, Ministry of Education of China, Beijing 100084, PR China and Tsinghua National ...;School of Software, Tsinghua University, Beijing 100084, PR China and Key Laboratory for Information System Security, Ministry of Education of China, Beijing 100084, PR China and Tsinghua National ...;School of Software, Tsinghua University, Beijing 100084, PR China and Department of Computer Science and Technology, Tsinghua University, Beijing 100084, PR China and Key Laboratory for Informatio ...;School of Software, Tsinghua University, Beijing 100084, PR China and Department of Computer Science and Technology, Tsinghua University, Beijing 100084, PR China and Key Laboratory for Informatio ...
Venue:
Computer-Aided Design
Year:
2011

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Abstract

This paper proposes an algorithm for calculating the orthogonal projection of parametric curves onto B-spline surfaces. It consists of a second order tracing method with which we construct a polyline to approximate the pre-image curve of the orthogonal projection curve in the parametric domain of the base surface. The final 3D approximate curve is obtained by mapping the approximate polyline onto the base surface. The Hausdorff distance between the exact orthogonal projection curve and the approximate curve is controlled under the user-specified distance tolerance. And the continuity of the approximate curve is @e"T-G^1, where @e"T is the user-specified angle tolerance. Experiments demonstrate that our algorithm is faster than the existing first order algorithms.