Analysis and avoidance of singularities for local G 1 surface interpolation of Bézier curve network with 4-valent nodes

Authors:
D.-Y. Cho;K.-Y. Lee;T.-W. Kim
Affiliations:
Seoul National University, Research Institute of Marine Systems Engineering, 151-741, Seoul, Korea;Seoul National University, Department of Naval Architecture and Ocean Engineering and Research Institute of Marine Systems Engineering, 151-741, Seoul, Korea;Seoul National University, Department of Naval Architecture and Ocean Engineering and Research Institute of Marine Systems Engineering, 151-741, Seoul, Korea
Venue:
Computing - Special issue on Geometric Modeling (Dagstuhl 2005)
Year:
2007

Citing 0
Cited 4

High-order approximation of implicit surfaces by G1 triangular spline surfaces

Computer-Aided Design
Local and singularity-free G 1 triangular spline surfaces using a minimum degree scheme

Computing - Geometric Modelling, Dagstuhl 2008
G1 Bézier surface generation from given boundary curve network with T-junction

GMP'10 Proceedings of the 6th international conference on Advances in Geometric Modeling and Processing
Constructing G1 Bézier surfaces over a boundary curve network with T-junctions

Computer-Aided Design

Quantified Score

Hi-index	0.00

Visualization

Abstract

We propose a local method of constructing piecewise G 1 Bézier patches to span a Bézier curve network with odd- and 4-valent node points. We analyze all possible singular cases of the G 1 condition that is to be met by the curve network interpolation and propose a new G 1 continuity condition using linear and quartic scalar weight functions. Using this condition, a curve network can be interpolated without modification at 4-valent nodes with two collinear tangent vectors, even in the presence of singularities. We demonstrate our approach by generating G 1 surfaces over the curve network which includes singularities at its node vertices and edges.