Closed-form Quadrangulation of N-Sided Patches

01/27/2021

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by   Marco Tarini, et al.

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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).