Out-of-core Constrained Delaunay Tetrahedralizations for Large Scenes

Abstract

Tetrahedralization algorithms are used for many applications such as Ray Tracing and Finite Element Methods. For most of the applications, constrained tetrahedralization algorithms are chosen because they can preserve input triangles. The constrained tetrahedralization algorithms developed so far might suffer from a lack of memory. We propose an out-of-core near Delaunay constrained tetrahedralization algorithm using the divide-and-conquer paradigm to decrease memory usage. If the expected memory usage is below the user-defined memory limit, we tetrahedralize using TetGen. Otherwise, we subdivide the set of input points into two halves and recursively apply the same idea to the two halves. When compared with the TetGen, our algorithm tetrahedralizes the point clouds using less amount of memory but takes more time and generates tetrahedralizations that do not satisfy the Delaunay criterion at the boundaries of the merged regions. We quantify the error using the aspect-ratio metric. The difference between the tetrahedralizations that our approach produce and the Delaunay tetrahedralization are small and the results are acceptable for most applications.