On $G^1$ stitched bi-cubic B\'ezier patches with arbitrary topology
Numerical Analysis
2017-09-12 v1
Abstract
Lower bounds on the generation of smooth bi-cubic surfaces imply that geometrically smooth () constructions need to satisfy conditions on the connectivity and layout. In particular, quadrilateral meshes of arbitrary topology can not in general be covered with -connected B\'ezier 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.
Keywords
Cite
@article{arxiv.1709.02994,
title = {On $G^1$ stitched bi-cubic B\'ezier patches with arbitrary topology},
author = {Jörg Peters},
journal= {arXiv preprint arXiv:1709.02994},
year = {2017}
}