Optimal Surface Parameterization Using Inverse Curvature Map

Mesh parameterization is a fundamental technique in computer graphics. The major goals during mesh parameterization are to minimize both the angle distortion and the area distortion. Angle distortion can be eliminated by the use of conformal mapping, in principle. Our paper focuses on solving the problem of finding the best discrete conformal mapping that also minimizes area distortion. First, we deduce an exact analytical differential formula to represent area distortion by curvature change in the discrete conformal mapping, giving a dynamic Poisson equation. On a mesh, the vertex curvature is related to edge lengths by the curvature map. Our result shows the map is invertible, i.e., the edge lengths can be computed from the curvature (by integration). Furthermore, we give the explicit Jacobi matrix of the inverse curvature map. Second, we formulate the task of computing conformal parameterizations with least area distortions as a constrained nonlinear optimization problem in curvatur...

• Type: Journal
• Year: 2008
• Where: TVCG
• Authors: Yong-Liang Yang, Junho Kim, Feng Luo 0002, Shi-Min Hu, Xianfeng Gu
• Keywords: Area Distortion, Conformal Mappings, Discrete Conformal Mappings, TVCG 2008