A mesh is locally quad-dominant (lqd) if all non-4-sided facets are surrounded by quadrilaterals. Lqd meshes allow for irregular nodes where $n\ne 4$ quads meet and for multi-sided facets, called T-gons, that end quad-strips and so adjust mesh density.

This paper introduces a new class of bi-cubic (bi-3) Geometric T-joint (GT) splines whose control nets are τ-nets, i.e. T-gons surrounded by quads. These GT-splines join smoothly with each other, bi-3 G-splines and regular $C^1$ bi-quadratic splines to form smooth surfaces of degree at most bi-3.

中文翻译：

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局部四元主导网格的低阶样条

如果所有非 4 边面都被四边形包围，则网格是局部四边形 (lqd)。Lqd 网格允许不规则节点，其中$n\ne 4$ 四边形相遇并用于多边面，称为 T 边形，结束四边形条带，因此可以调整网格密度。

本文介绍了一类新的双三次 (bi-3) 几何 T 型接头 (GT) 样条，其控制网络是τ网络，即四边形包围的 T 边形。这些 GT 样条相互平滑地连接，双 3 G 样条和规则$C^1$ 双二次样条以形成阶数最多为 bi-3 的光滑表面。