Controllable curl-correction of 3D frame fields

Abstract

Hexahedral meshes represent an attractive discretization strategy in finite element analyses owing to their good numerical performance. Frame field-based remeshing is an important technique for controllable hexahedral meshing. Existing frame-field generation methods cannot be directly used for purely hexahedral meshing due to possible topological conflicts. These problems are less severe in the case of hexahedral-dominant meshing. However, the quality of these hexahedral-dominant meshes is largely affected by the curl of the input frame fields. With the aim of overcoming this issue, we propose a direction-preserving and length-controllable curl-correction method of 3D frame fields. We analyze and construct the discretized curl energy of the 3D vector field on tetrahedral meshes and extend it to frame fields, i.e., the composition of three vector fields. In order to preserve the input directions as much as possible, three scalar fields were introduced to denote the stretch length of the three vectors of the frame fields and represent the new fields as a combination of the original frame fields and scalar fields. Through global-optimization of the curl energy combined with a smooth term, the final curl-corrected frame fields are obtained, which are further used for hexahedral-dominant remeshing. The results indicate that the proposed method can reduce the curl of the frame fields efficiently while keeping their directions as well as controlling the extent of their length. By applying such frame fields to existing hexahedral-dominant remeshing methods, direction- and size-controllable hexahedral-dominant meshes can be obtained. Besides, the proposed method deduces to a convex quadratic programming problem with simple box constraints, which is easy-to-solve.