基于网格平行性的离散曲面曲率理论
A curvature theory for discrete surfaces based on mesh parallelity
摘要：
本文研究了具有边向平行高斯像的离散曲面曲率的一般理论，其中面的平均曲率和高斯曲率由面的面积和混合面积导出。值得注意的是，这些概念能够统一之前定义的著名曲面类别，例如离散等温极小曲面和恒定中曲率的曲面。我们讨论了各种类型的自然高斯图像，存在的主曲率，常曲率曲面，Christoffel对偶，柯尼希斯网，接触元网，s-等温网，和有趣的特殊情况下，如离散Delaunay表面来自椭圆台球。
英文摘要：
We consider a general theory of curvatures of discrete surfaces equipped with edgewise parallel Gauss images, and where mean and Gaussian curvatures of faces are derived from the faces' areas and mixed areas. Remarkably these notions are capable of unifying notable previously defined classes of surfaces, such as discrete isothermic minimal surfaces and surfaces of constant mean curvature. We discuss various types of natural Gauss images, the existence of principal curvatures, constant curvature surfaces, Christoffel duality, Koenigs nets, contact element nets, s-isothermic nets, and interesting special cases such as discrete Delaunay surfaces derived from elliptic billiards.
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