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.

中文翻译：

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N面贴片的闭合形式四边形

我们分析了对四边形的$ n $面片进行四边形化的问题，在其边界处有规定数量的边缘细分，并且有一个内部不规则顶点（没有，当n = 4 $时）打破了原本完全规则的晶格。我们以解析闭合形式得出：（1）补丁必须满足的必要条件和充分条件才能接受此四边形，以及（2）对所得细分的完整描述。