Efficient and High Quality Contouring of Isosurfaces on Uniform Grids

The interactive polygonization of isosurfaces has become possible with the mapping of the marching cubes (MC) and marching tetrahedra (MT) algorithms to GPUs. Such mapping is not as straightforward in cases that the algorithm generate meshes closer to the isosurface or result in better polygon shapes, since they often require complex computations for the vertex positioning of the polygons or even do not have table-driven implementations. In this paper, we revisit dual contouring (DC) and Macet algorithms and propose, respectively: (i) a novel parallel efficient version on uniform grids and (ii) novel GPU modules which extend the original MC. Our DC algorithm is table-driven and positions the vertices in a particle-based fashion, which is then used to map into a GPU implementation. In addition, we enumerate the current ways to implement efficient contouring algorithms on the GPUs as orthogonal features, and present the tradeoff of each approach. We validate the efficiency of our algorithms with its comparison to interactive versions of MC algorithms.