Closed-form Quadrangulation of N-Sided Patches

Marco Tarini

doi:10.1016/j.cag.2022.06.015

paper

Closed-form Quadrangulation of N-Sided Patches

arXiv:2101.11569 · doi:10.1016/j.cag.2022.06.015

Abstract

We analyze the problem of quadrangulating a $n$ -sided patch, each side at its boundary subdivided into a given number of edges, using a single irregular vertex (or none, when $n = 4$ ) that breaks the otherwise fully regular lattice. We derive, in an analytical closed-form, (1) the necessary and sufficient conditions that a patch must meet to admit this quadrangulation, and (2) a full description of the resulting tessellation(s).