Robust One-to-One Sweeping with Harmonic S-T Mappings and Cages

A sweeping algorithm can generate hexahedral meshes by sweeping an all-quad mesh on the source surface to the target surface. For one-toone sweeping, the most difficult thing is to generate an all-quad mesh on the target surface which has the same mesh connectivity as that of the source surface. The traditional method is to use the affine transformation, like translation, rotation, scaling or combinations of them. This method works very well on the convex cases, while it fails for concave and multiply-connected surfaces. In this paper, harmonic function is used to map meshes from a source surface to its target surface. The result shows that it can generate an all-quad mesh on the target surface with good quality without any inverted elements and thus avoid expensive smoothing algorithm (untangling). In order to generate interior nodes between the source and target surface, cage-based deformation method is applied with good mesh quality as well.