论文标题
Penner坐标中的度量优化
Metric Optimization in Penner Coordinates
论文作者
论文摘要
几何处理中的许多参数化和与映射有关的问题可以看作是度量优化问题，即计算最小化功能并满足一组约束（例如平面度）的度量度量。彭纳（Penner）坐标是与固定顶点集和拓扑的网格指标空间上的全局坐标，但连通性有所不同，使其同构对欧几里得尺寸的尺寸空间等于网格中边缘的数量，而没有任何其他约束。这些坐标在离散的共形图理论中起着重要的作用，从而使高度鲁棒算法的最新发展具有收敛性和解决方案的存在，可以保证计算此类地图。我们演示了如何使用Penner坐标来解决涉及指标的一般优化问题，包括优化和插值，同时保留关键解决方案存在保证可用于离散的共形图。
Many parametrization and mapping-related problems in geometry processing can be viewed as metric optimization problems, i.e., computing a metric minimizing a functional and satisfying a set of constraints, such as flatness. Penner coordinates are global coordinates on the space of metrics on meshes with a fixed vertex set and topology, but varying connectivity, making it homeomorphic to the Euclidean space of dimension equal to the number of edges in the mesh, without any additional constraints imposed. These coordinates play an important role in the theory of discrete conformal maps, enabling recent development of highly robust algorithms with convergence and solution existence guarantees for computing such maps. We demonstrate how Penner coordinates can be used to solve a general class of optimization problems involving metrics, including optimization and interpolation, while retaining the key solution existence guarantees available for discrete conformal maps.
