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).

翻译：我们分析了四分五裂的问题,在边界上,每一方的边界被细分为一定数量的边缘,使用一个打破原本完全正常的顶层的单一非正常的顶部(或无,当美元=4美元时),我们用分析封闭形式得出:(1) 补丁必须满足的必要和充分条件才能承认这一四分形,(2) 完整地描述由此产生的熔化。