基于极多面体概念的离散外在曲率
Discrete extrinsic curvatures based on polar polyhedra concept
AI总结：
本文利用局部极多面体序列构造球面高斯映射的分片仿射逼近，得到平均曲率和高斯曲率的逐点收敛逼近，并实现弯曲能量的自然离散化。
摘要：
几何对象逼近的对偶原理（也称为Eudoxus穷举法）由阿基米德在其著名论文《圆的测量》中扩展和完善。阿基米德逼近方法的主要思想是构造一系列内接和外接多边形（多面体）对，以逼近曲线凸体。该序列允许逼近曲线的长度以及物体的面积和体积，并获得逼近的误差估计。本文表明，局部极多面体对的序列允许构造球面高斯映射的分片仿射逼近，构造平均曲率和高斯曲率的逐点收敛逼近，以及获得弯曲能量的自然离散化。
英文摘要：
Duality principle for approximation of geometrical objects (also known as Eudoxus exhaustion method) was extended and perfected by Archimedes in his famous tractate "Measurement of circle". The main idea of the approximation method by Archimedes is to construct a sequence of pairs of inscribed and circumscribed polygons (polyhedra) which approximate curvilinear convex body. This sequence allows to approximate length of curve, as well as area and volume of the bodies and to obtain error estimates for approximation. In this work it is shown that a sequence of pairs of locally polar polyhedra allows to construct piecewise-affine approximation to scherical Gauss map, to construct convergent point-wise approximations to mean and Gauss curvature, as well as to obtain natural discretizations of bending energies.
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。
