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...
Three-dimensional symmetric tensor fields have a wide range of applications in solid and fluid mechanics. Recent advances in the topological analysis of 3D symmetric tensor fields focus on the local behaviors of tensor fields at degenerate points, which usually form curves. In this paper, we make a number of observations...
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...