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arXiv · 1709.02994

On $G^1$ stitched bi-cubic Bézier patches with arbitrary topology

Jörg Peters
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Abstract

Lower bounds on the generation of smooth bi-cubic surfaces imply that geometrically smooth ($G^1$) constructions need to satisfy conditions on the connectivity and layout. In particular, quadrilateral meshes of arbitrary topology can not in general be covered with $G^1$ -connected Bézier patches of bi-degree 3 using the layout proposed in [ASC17]. This paper analyzes whether the pre-refinement of the input mesh by repeated Doo-Sabin subdivision proposed in that paper yields an exception.

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Jörg Peters. 2017-09-09. On $G^1$ stitched bi-cubic Bézier patches with arbitrary topology. https://arxiv.org/abs/1709.02994

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