期刊
COMPUTER AIDED GEOMETRIC DESIGN
卷 29, 期 5, 页码 219-230出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cagd.2011.10.003
关键词
Network of curves; Interpolation; C-2 surface; Vertex enclosure constraint; G(2) Euler condition
资金
- NSF [CCF-0728797]
- Direct For Computer & Info Scie & Enginr
- Division of Computing and Communication Foundations [1117695] Funding Source: National Science Foundation
Prescribing a network of curves to be interpolated by a surface model is a standard approach in geometric design. Where it curves meet, even when they afford a common normal direction, they need to satisfy an algebraic condition, called the vertex enclosure constraint, to allow for an interpolating piecewise polynomial C-1 surface. Here we prove the existence of an additional, more subtle constraint that governs the admissibility of curve networks for G(2) interpolation. Additionally, analogous to the first-order case but using the Monge representation of surfaces, we give a sufficient geometric, G(2) Euler condition on the curve network. When satisfied, this condition guarantees existence of an interpolating surface. Crown Copyright (C) 2011 Published by Elsevier B.V. All rights reserved.
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