We propose a new surface representation, the Generalized B-spline (GBS) patch, that combines ribbon interpolants given in B-spline form. A GBS patch can connect to tensor-product B-spline surfaces with arbitrary $G^m$ continuity. It supports ribbons not only along the perimeter loop, but also around holes in the interior of the patches.

This is a follow-up paper of a recent publication (Várady et al., 2020) that described multi-sided Bézier surfaces over curved multi-sided domains. While the fundamental concept is retained, several new details have been elaborated. The weighting functions are modified to be products of B-spline and Bernstein basis functions, multiplied by rational terms. A new local parameterization method is introduced using harmonic functions, that handles periodic hole loops, as well. Interior shape control is adapted to the B-spline representation of the ribbons. Several examples illustrate the capabilities of the proposed scheme. Our implementation is based on a computationally efficient discretization.

我们提出了一种新的表面表示，即广义 B 样条 (GBS) 补丁，它结合了以 B 样条形式给出的带状插值。GBS 贴片可以连接到任意的张量积 B 样条曲面$G^{米}$连续性。它不仅支持沿着周边环的色带，还支持贴片内部孔周围的色带。

这是最近出版物（Várady 等人，2020 年）的后续论文，该论文描述了弯曲多边域上的多边贝塞尔曲面。在保留基本概念的同时，还详细阐述了一些新的细节。加权函数被修改为 B 样条和伯恩斯坦基函数的乘积，乘以有理项。使用谐波函数引入了一种新的局部参数化方法，该方法也处理周期性孔环。内部形状控制适用于色带的 B 样条表示。几个例子说明了所提议方案的能力。我们的实现基于计算高效的离散化。