We analyze the problem of quadtragulating a n-sided patch, with prescribed numbers of edge-subdivisions at its boundary , with a single internal irregular vertex (  none, when n = 4) breaking the otherwise fully regular lattice. We derive, in  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  .
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) .
R
quadtragulating
quadrangulating
R
with prescribed numbers of edge-subdivisions
each side
R
, with a single internal
subdivided into a given number of edges, using a single
A
or
R
breaking
that breaks
A
an
A
(s)