复曲面曲面片控制点的一些几何问题
Some geometrical aspects of control points for toric patches
摘要：
我们使用代数几何和动力系统的思想来解释控制点影响贝塞尔曲线或曲面片形状的一些方式。特别地，我们建立了Birch定理的一个推广，并利用它导出了曲面片为内射的控制点的充分条件。我们还解释了一种方法，控制点的影响，通过退化到规则的控制多面体的形状。本文研究的自然对象是无理曲面片，它是Krasauskas复曲面片的推广，并包括Bézier曲面片和张量积曲面片作为重要的特例。
英文摘要：
We use ideas from algebraic geometry and dynamical systems to explain some ways that control points influence the shape of a Bézier curve or patch. In particular, we establish a generalization of Birch's Theorem and use it to deduce sufficient conditions on the control points for a patch to be injective. We also explain a way that the control points influence the shape via degenerations to regular control polytopes. The natural objects of this investigation are irrational patches, which are a generalization of Krasauskas's toric patches, and include Bézier and tensor product patches as important special cases.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
