G2 Surface Interpolation Over General Topology Curve Networks

The basic idea of curve network‐based design is to construct smoothly connected surface patches, that interpolate boundaries and cross‐derivatives extracted from the curve network. While the majority of applications demands only tangent plane (G1) continuity between the adjacent patches, curvature c...

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Bibliographic Details
Published in:	Computer graphics forum Vol. 33; no. 7; pp. 151 - 160
Main Authors:	Salvi, Péter, Várady, Tamás
Format:	Journal Article
Language:	English
Published:	Oxford Blackwell Publishing Ltd 01.10.2014
Subjects:	Analysis Categories and Subject Descriptors (according to ACM CCS) Computer graphics Computer Graphics [I.3.5]: Computational Geometry and Object Modeling-curvenet-based design Computer Graphics [I.3.5]: Computational Geometry and Object Modeling—curvenet‐based design, transfinite surfaces, Gregory patches, G2 continuity G2 continuity Gregory patches Network topologies Optimization Studies Topological manifolds transfinite surfaces
ISSN:	0167-7055, 1467-8659
Online Access:	Get full text
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Summary:	The basic idea of curve network‐based design is to construct smoothly connected surface patches, that interpolate boundaries and cross‐derivatives extracted from the curve network. While the majority of applications demands only tangent plane (G1) continuity between the adjacent patches, curvature continuous connections (G2) may also be required. Examples include special curve network configurations with supplemented internal edges, “master‐slave” curvature constraints, and general topology surface approximations over meshes. The first step is to assign optimal surface curvatures to the nodes of the curve network; we discuss different optimization procedures for various types of nodes. Then interpolant surfaces called parabolic ribbons are created along the patch boundaries, which carry first and second derivative constraints. Our construction guarantees that the neighboring ribbons, and thus the respective transfinite patches, will be G2 continuous. We extend Gregory's multi‐sided surface scheme in order to handle parabolic ribbons, involving the blending functions, and a new sweepline parameterization. A few simple examples conclude the paper.
Bibliography:	ark:/67375/WNG-XBTVDCWZ-4 istex:958A7754261E395FCB1134130228C96C8A77D0E9 ArticleID:CGF12483 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14
ISSN:	0167-7055 1467-8659
DOI:	10.1111/cgf.12483