Traditionally the approach to filling n-sided holes differs substantially for bicubic $C^2$-splines vs biquadratic $C^1$-splines due to the ‘primal’ vs ‘dual’ interpretation of the control net that emphasizes either n-valent vertices or n-sided facets. Here we propose a construction that unites the treatment of both types of spline surfaces, notably for non-4-valent vertices in a quad-layout. The primal-dual-agnostic multi-sided surfaces are of degree bi-4. Their main body can be chosen to be $C^1$ or $C^2$ and the remaining gap is filled by a tiny central $G^1$ cap.

中文翻译：

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C ² bi-3和C ¹ bi-2花键的多面完成：统一方法

传统上，填充n边孔的方法对于双三次方大不相同$C^{\mathrm{2个}}$样条曲线与双二次曲线 $C^{\mathrm{1个}}$样条线是由于对控制网的“原始”与“双重”解释而强调了n个价顶点或n个侧面。在这里，我们提出了一种构造，它将两种类型的样条曲面的处理统一起来，特别是对于四布局中的非4价顶点。不可知论的双面表面的度数为bi-4。他们的主体可以被选择为$C^{\mathrm{1个}}$ 或者 $C^{\mathrm{2个}}$ 剩余的空白由一个微小的中央填充 $G^{\mathrm{1个}}$ 帽。