31 citations · 80 across the 22 of their papers we have counts for
13 papers · 1 filter
Rigidity of the Delaunay triangulations of the plane
Song Dai, Tianqi Wu
We proved a rigidity result for Delaunay triangulations of the plane under Luo's discrete conformal change, extending previous results on hexagonal triangulations. Our result is a…
Rigidity of Acute Triangulations of the Plane
Tianqi Wu
We show that a uniformly acute triangulation of the plane is rigid under Luo's discrete conformal change, extending previous results on hexagonal triangulations. Our result is a di…
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…
Fractional combinatorial Calabi flow on surfaces
Tianqi Wu, Xu Xu
Using the fractional discrete Laplace operator for triangle meshes, we introduce a fractional combinatorial Calabi flow for discrete conformal structures on surfaces, which unifies…
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…
Discrete Conformal Geometry of Polyhedral Surfaces and Its Convergence
Feng Luo, Jian Sun, Tianqi Wu
The paper proves a result on the convergence of discrete conformal maps to the Riemann mappings for Jordan domains. It is a counterpart of Rodin-Sullivan's theorem on convergence o…
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…
Koebe conjecture and the Weyl problem for convex surfaces in hyperbolic 3-space
Feng Luo, Tianqi Wu
We prove that the Koebe circle domain conjecture is equivalent to the Weyl type problem that every complete hyperbolic surface of genus zero is isometric to the boundary of the hyp…
A discrete uniformization theorem for polyhedral surfaces II
Xianfeng Gu, Ren Guo, Feng Luo +2
A discrete conformality for hyperbolic polyhedral surfaces is introduced in this paper. This discrete conformality is shown to be computable. It is proved that each hyperbolic poly…
A discrete uniformization theorem for polyhedral surfaces
Xianfeng Gu, Feng Luo, Jian Sun +1
A discrete conformality for polyhedral metrics on surfaces is introduced in this paper which generalizes earlier work on the subject. It is shown that each polyhedral metric on a s…
Rigidity of Infinite Hexagonal Triangulation of the Plane
Tianqi Wu, Xianfeng Gu, Jian Sun
In the paper, we consider the rigidity problem of the infinite hexagonal triangulation of the plane under the piecewise linear conformal changes introduced by Luo in [5]. Our resul…