In this paper we introduce hexagonal global parameterizations, a new type of parameterization in which parameter lines respect six-fold rotational symmetries (6-RoSy). Such parameterizations enable the tiling of surfaces with regular hexagonal texture and geometry patterns and can be used to generate high-quality triangular remeshing. To construct a hexagonal parameterization...
The P1 discretization of the Laplace operator on a triangulated
polyhedral surface is related to geometric properties of the surface. This paper studies extremum problems for eigenvalues of the P1 discretization of the
Laplace operator. Among all triangles, an equilateral triangle has the maximal first positive eigenvalue. Among all cyclic...
Branched covering spaces are a mathematical concept which originates from complex analysis and topology and has found applications in tensor field topology and geometry re-meshing. Given a manifold surface and an N-way rotational symmetry field, a branched covering space is a manifold surface that has an N-to-1 map to the...
Many applications in computer graphics and geometry processing rely on the ability to
locally orient 2D and 3D entities on a surface, or inside a volume, such as the sinusoidal
kernels in Gabor noise, the color and geometry textures in pattern synthesis, and the
finite elements in remeshing. In these...