6 papers
A Discrete-to-Continuum Variational Theory for Area-Preserving Surface Parameterization
Shu-Yung Liu, Kento Sakai, Mei-Heng Yueh
We establish a discrete-to-continuum variational theory for area-preserving parameterization of surfaces based on the stretch energy. For orientation-preserving diffeomorphisms bet…
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…
Volume-Preserving Parameterizations via Preconditioned Nonlinear Conjugate Gradient Method
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 canonical domain while preserving local volume. We formulate this problem as an unconstrai…
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…