论文标题
计算谐波图和点云上的共形图
Computing Harmonic Maps and Conformal Maps on Point Clouds
论文作者
论文摘要
我们提出了一种新型的无网格方法，用于计算仅使用点云数据嵌入欧几里得3空间中嵌入在欧几里得3空间中的谐波图和保形图。给定表面或点云的近似，我们只使用标准立方晶格来近似其$ε$ - 纽伯特。然后，可以通过晶格上的离散谐波图近似表面的谐波图。共形图或表面均匀化是通过最小化谐波图的差异能量而实现的，同时变形了恒定曲率的目标表面。我们提出了有关封闭表面和拓扑磁盘的算法和数值示例。
We propose a novel meshless method to compute harmonic maps and conformal maps for surfaces embedded in the Euclidean 3-space, using point cloud data only. Given a surface, or a point cloud approximation, we simply use the standard cubic lattice to approximate its $ε$-neighborhood. Then the harmonic map of the surface can be approximated by discrete harmonic maps on lattices. The conformal map, or the surface uniformization, is achieved by minimizing the Dirichlet energy of the harmonic map while deforming the target surface of constant curvature. We propose algorithms and numerical examples for closed surfaces and topological disks.
