4 research outputs found
A unified framework for isotropic meshing based on narrow-band Euclidean distance transformation
In this paper, we propose a simple-yet-effective method for isotropic meshing relying on Euclidean distance transformation based centroidal Voronoi tessellation (CVT). Our approach improves the performance and robustness of computing CVT on curved domains while simultaneously providing high-quality output meshes. While conventional extrinsic methods compute CVTs in the entire volume bounded by the input model, we restrict the computation to a 3D shell of user-controlled thickness. Taking voxels which contain surface samples as sites, we compute the exact Euclidean distance transform on the GPU. Our algorithm is parallel and memory-efficient, and can construct the shell space for resolutions up to 20483 at interactive speed. The 3D centroidal Voronoi tessellation and restricted Voronoi diagrams are also computed efficiently on the GPU. Since the shell space can bridge holes and gaps smaller than a certain tolerance, and tolerate non-manifold edges and degenerate triangles, our algorithm can handle models with such defects, which typically cause conventional remeshing methods to fail. Our method can process implicit surfaces, polyhedral surfaces, and point clouds in a unified framework. Computational results show that our GPU-based isotropic meshing algorithm produces results comparable to state-of- the-art techniques, but is significantly faster than conventional CPU-based implementations.MOE (Min. of Education, S’pore)Published versio
Layered Fields for Natural Tessellations on Surfaces
Mimicking natural tessellation patterns is a fascinating multi-disciplinary
problem. Geometric methods aiming at reproducing such partitions on surface
meshes are commonly based on the Voronoi model and its variants, and are often
faced with challenging issues such as metric estimation, geometric, topological
complications, and most critically parallelization. In this paper, we introduce
an alternate model which may be of value for resolving these issues. We drop
the assumption that regions need to be separated by lines. Instead, we regard
region boundaries as narrow bands and we model the partition as a set of smooth
functions layered over the surface. Given an initial set of seeds or regions,
the partition emerges as the solution of a time dependent set of partial
differential equations describing concurrently evolving fronts on the surface.
Our solution does not require geodesic estimation, elaborate numerical solvers,
or complicated bookkeeping data structures. The cost per time-iteration is
dominated by the multiplication and addition of two sparse matrices. Extension
of our approach in a Lloyd's algorithm fashion can be easily achieved and the
extraction of the dual mesh can be conveniently preformed in parallel through
matrix algebra. As our approach relies mainly on basic linear algebra kernels,
it lends itself to efficient implementation on modern graphics hardware.Comment: Natural tessellations, surface fields, Voronoi diagrams, Lloyd's
algorith