An octree-based dual contouring method for triangular and tetrahedral mesh generation with guaranteed angle range

This paper presents a novel octree-based dual contouring (DC) algorithm for adaptive triangular or tetrahedral mesh generation with guaranteed angle range. First, an adaptive octree is constructed based on the input geometry. Then the octree grid points are adjusted such that we can maintain a minimum distance from the grid points to the input boundary. Finally, an improved DC method is applied to generate triangular and tetrahedral meshes. It is proved that we can guarantee the obtained triangle mesh has an angle range of (19.47A degrees, 141.06A degrees) for any closed smooth curve, and the tetrahedral mesh has a dihedral angle range of (12.04A degrees, 129.25A degrees) for any closed smooth surface. In practice, since the straight line/planar cutting plane assumption inside each octree leaf is not always satisfied, there is a small perturbation for the lower and upper bounds of the proved angle range.