2024/12/13 by Shu-Yung Liu, Liu, Shu-Yung, Mei-Heng Yueh +1 · 1 citation
Engineering · #Advanced optical system design
paper · pdf · doi:10.48550/arxiv.2412.09909
Surface parameterization is a fundamental concept in fields such as\ndifferential geometry and computer graphics. It involves mapping a surface in\nthree-dimensional space onto a two-dimensional parameter space. This process\nallows for the systematic representation and manipulation of surfaces of\ncomplicated shapes by simplifying them into a manageable planar domain. In this\npaper, we propose a new iterative algorithm for computing the parameterization\nof simply connected open surfaces that achieves an optimal balance between\nangle and area distortions. We rigorously prove that the iteration in our\nalgorithm converges globally, and numerical results demonstrate that the\nresulting mappings are bijective and effectively balance angular and area\naccuracy across various triangular meshes. Additionally, we present the\npractical usefulness of the proposed algorithm by applying it to represent\nsurfaces as geometry images.\n