high performance computing on graphics processing units: hgpu.org

In this paper, we propose to extend high quality Centroidal Voronoi Tessellation (CVT) remeshing techniques to the case of surfaces which are not defined by triangle meshes, such as implicit surfaces. Our key observation is that rasterization routines are usually available to visualize these alternative representations, most often as OpenGL shaders efficiently producing surface samples (fragments) from the surface representation. Our technique has the ability to mesh any surface for which rasterization routines are available, and runs entirely within the OpenGL rasterization pipeline. There is no intermediate representation: the triangle mesh is computed directly from the surface fragments. Our method produces high quality meshes, as it inherits the properties of CVT meshing. Contrary to existing GPU techniques for CVT computation, it does not require a surface parameterization, and it extracts the mesh topology directly from the surface fragments. Optionally, our algorithm can produce two-manifold, consistently oriented meshes. We describe our complete implementation and show a variety of applications: direct meshing of implicit surfaces, meshing of operations between solids, mesh repair, and solid sculpting. We analyze performance, correctness and mesh quality.