On G¹ stitched bi-cubic Bézier patches with arbitrary topology

2017/09/09 by Peters, Jörg
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1709.02994

Abstract

Lower bounds on the generation of smooth bi-cubic surfaces imply that geometrically smooth (G¹) constructions need to satisfy conditions on the connectivity and layout. In particular, quadrilateral meshes of arbitrary topology can not in general be covered with G¹ -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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