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.

翻译：我们分析一个四分法的问题,即四分法以一个单一的内部非常规脊椎(无,当一美元=4美元时)打破原本完全正常的顶层。 我们从分析封闭形式中得出:(1) 补丁必须满足的必要和充分条件才能承认这一四分法,(2) 全面描述由此导致的熔化。