-G2 B-spline surface interpolation

Authors:
Kan-Le Shi;Jun-Hai Yong;Jia-Guang Sun;Jean-Claude Paul
Affiliations:
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 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 Key Laboratory for Information System Security, Ministry of Education of China, Beijing 100084, PR China and Tsinghua National ...
Venue:
Computer Aided Geometric Design
Year:
2011

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Abstract

This paper proposes a method to construct a B-spline surface that interpolates the specified four groups of boundary derivative curves in the B-spline form. The discontinuity can be bounded by an arbitrary geometric invariant @e- as the tolerance. The method first handles the six types of the compatibility problems by continuity-preserving reparameterization, knot-insertion and local control-point tuning. The transformed boundary conditions are then parametrically compatible, so the Coons strategy can be applied to construct the final interpolant. Not only can it be used in the reliable geometric modeling, but the approach also can be applied to many other algorithms that require compatibility guarantee.