6 citations · 12 across the 6 of their papers we have counts for
7 papers
Hexagonal Geometric Triangulations
Yanwen Luo, Xiaoping Zhu, Tianqi Wu
It is well-known that the Euclidean plane has a standard 6-regular geodesic triangulation , and the unit sphere has a 5-regular geodesic triangulation, which is induced from the re…
Spaces of Geodesic Triangulations Are Cells
Yanwen Luo, Zhenghao Rao, Tianqi Wu +1
It has been shown that spaces of geodesic triangulations of closed negatively curved surfaces are contractible. Here we prove that these spaces are homeomorphic to Euclidean spaces…
The Deformation Space of Delaunay Triangulations of the Sphere
Yanwen Luo, Tianqi Wu, Xiaoping Zhu
In this paper, we determine the topology of the spaces of convex polyhedra inscribed in the unit -sphere and the spaces of strictly Delaunay geodesic triangulations of the unit…
The Convergence of Discrete Uniformizations for Genus Zero Surfaces
Yanwen Luo, Tianqi Wu, Xiaoping Zhu
The notion of discrete conformality proposed by Luo and Bobenko-Pinkall-Springborn on triangle meshes has rich mathematical theories and wide applications. Gu et al. proved that th…
The Deformation Spaces of Geodesic Triangulations of Flat Tori
Yanwen Luo, Tianqi Wu, Xiaoping Zhu
We prove that the deformation space of geodesic triangulations of a flat torus is homotopy equivalent to a torus. This solves an open problem proposed by Connelly et al. in 1983, i…
The Deformation Space of Geodesic Triangulations and Generalized Tutte's Embedding Theorem
Yanwen Luo, Tianqi Wu, Xiaoping Zhu
We proved the contractibility of the deformation space of the geodesic triangulations on a closed surface of negative curvature. This solves an open problem proposed by Connelly et…
The Convergence of Discrete Uniformizations for Closed Surfaces
Tianqi Wu, Xiaoping Zhu
The notions of discrete conformality on triangle meshes have rich mathematical theories and wide applications. The related notions of discrete uniformizations on triangle meshes, s…