4 papers
Discrete minimal surfaces: Old and New
Wai Yeung Lam, Masashi Yasumoto
We survey structure-preserving discretizations of minimal surfaces in Euclidean space. Our focus is on a discretization defined via parallel face offsets of polyhedral surfaces, wh…
Infinite circle patterns in the Weil-Petersson class
Wai Yeung Lam
Analogous to Weil-Petersson quasicircles, we investigate infinite circle patterns in the Euclidean plane parameterized by discrete harmonic functions of finite Dirichlet energy. Th…
Period matrices and homological quasi-trees on discrete Riemann surfaces
Wai Yeung Lam, On-Hei Solomon Lo, Chi Ho Yuen
We study discrete period matrices associated with graphs cellularly embedded on closed surfaces, resembling classical period matrices of Riemann surfaces. Defined via integrals of…
A Structure-Preserving Numerical Method for Harmonic Maps Between High-genus Surfaces
Zhipeng Zhu, Wai Yeung Lam, Lok Ming Lui
Motivated by geometry processing for surfaces with non-trivial topology, we study discrete harmonic maps between closed surfaces of genus at least two. Harmonic maps provide a natu…