6 papers
Area-Preserving Parameterization: Variational Principle, Gradient Flow, and Discrete Approximation
Shu-Yung Liu, Kento Sakai, Mei-Heng Yueh
Area-preserving parameterizations are used in applications where relative surface areas must be preserved. We study this problem through the stretch energy. For orientation-preserv…
Square-Domain Area-Preserving Parameterization for Genus-Zero and Genus-One Closed Surfaces
Shu-Yung Liu, Mei-Heng Yueh
The parameterization of closed surfaces typically requires either multiple charts or a non-planar domain to achieve a seamless global mapping. In this paper, we propose a numerical…
Energy-Based Distortion-Balancing Parameterization for Open Surfaces
Shu-Yung Liu, Mei-Heng Yueh
Surface parameterization is a fundamental concept in fields such as differential geometry and computer graphics. It involves mapping a surface in three-dimensional space onto a two…
Spherical Area-Preserving Parameterization via Energy Minimization
Shu-Yung Liu, Mei-Heng Yueh
We propose a novel method, called spherical authalic energy minimization (SAEM), for computing spherical area-preserving parameterizations of genus-zero closed surfaces, with stron…
Isovolumetric Energy Minimization for Ball-Shaped Volume-Preserving Parameterizations of 3-Manifolds
Shu-Yung Liu, Tsung-Ming Huang, Wen-Wei Lin +1
A volume-preserving parameterization is a bijective mapping that maps a 3-manifold onto a specified canonical domain that preserves the local volume. This paper formulates the comp…
Convergent Authalic Energy Minimization for Disk Area-Preserving Parameterizations
Shu-Yung Liu, Mei-Heng Yueh
An area-preserving parameterization is a bijective mapping that maps a surface onto a specified domain and preserves the local area. This paper formulates the computation of disk a…