Optimized Bounding Polyhedra For GPU-Based Distance Transform

Many problems in areas such as computer graphics, scientific visualization, computational geometry, or image processing require the computation of a distance field. The distance field indicates at each point in space the shortest distance to a given object. Depending on the problem setting, the object is described either by a voxel attribute within a volume data set or by a surface representation such as a triangle mesh. The two cases require separate approaches, and only the case of the triangle mesh is studied in this paper. Often, the distance field is needed as a regular grid of samples. The samples can be computed either in image space or object space, referring to the outer loop of the algorithm, which iterates over all samples or all triangles of the mesh, respectively. Object space methods can be competitive, especially for higher resolutions. An ideal object space method would compute a generalized Voronoi diagram (GVD) of the mesh and then scan convert its cells. At each sample location, the distance to the Voronoi site associated with the cell would yield the field value. A practical method however, avoids the expensive GVD computation and instead works with bounding polyhedra for the Voronoi cells. In this paper, we propose a new type of bounding polyhedra. This reduces the number of polyhedra and simplifies their geometry. The choice of these bounding polyhedra pays off especially if scan conversion is run on graphics hardware.