Finely-Threaded History-Based Topology Computation

Graphics and visualization pipelines often make use of highly parallelized algorithms which transform an input mesh into an output mesh. One example is Marching Cubes, which transforms a voxel grid into a triangle mesh approximation of an isosurface. These techniques often discard the topological connectivity of the output mesh, and instead produce a 'soup' of disconnected geometric elements. Calculations that require local neighborhood, such as surface curvature, cannot be performed on such outputs without first reconstructing its topology. We present a novel method for reconstructing topological information across several kinds of mesh transformations, which we demonstrate with GPU and OpenMP implementations. Our approach makes use of input topological elements for efficient location of coincident elements in the output. We provide performance data for the technique for isosurface generation, tetrahedralization, subdivision, and dual mesh generation, and demonstrate its use in visualization pipelines containing further computations of local curvature and mesh coarsening.