English

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 (G1G^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 G1G^1 -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}
}