Reproduce “Spherical Conformal Parameterization of Genus-0 Point Clouds for Meshing” on OpenResearch
Turn your favorite coding agents into research agents that review literature, develop hypotheses, and run experiments.
Universal app for Apple silicon and Intel. Requires macOS 11 or later.
About this paper
Gary Pui-Tung Choi, Kin Tat Ho, Lok Ming Lui
A framework is developed for generating high-quality mesh structures from genus-0 point clouds using spherical conformal parameterization. The approach achieved a 25% reduction in maximum position errors for Laplace-Beltrami approximation and produced meshes with better conformality and higher Delaunay ratios (0.99-1.00) compared to existing methods.
Key insights
- The accuracy of Laplace-Beltrami operator approximation on point clouds can be enhanced through a specific Gaussian-type weight function within the MLS framework, crucial for conformal mapping.
- Conformal parameterization can be robustly achieved on point clouds using an iterative scheme (North-South reiteration) that relies solely on solving Laplace equations, effectively improving conformality without complex quasi-conformal computations.
- Achieving a balanced distribution of points in the spherical parameterization is important for high-quality mesh generation, which can be addressed by a scaling factor derived from geometric invariance properties.
Summary by alphaXiv.
Tip: change arxiv.org to autoarxiv.org in any arXiv abstract link to open the paper here.