Structure-aware geometric optimization of hexahedral mesh

Abstract

Current geometric optimization methods do not fully consider the overall structure of the model, which may make the effect of geometric optimization of the hex meshes for the models with concave curves unsatisfactory. To this end, this paper proposes an approach to structure-aware geometric optimization of hex meshes. In the approach, by relocating the position of the base complex of the hex mesh, the overall parameterized energy is reduced to obtain an optimized geometric embedding. First, a frame field which conforms to the base complex structure of the input hex mesh is generated. Then, a parameterization that satisfies the structure constraints is established based on the frame field. Finally, the positions of the singular lines of the hex mesh are optimized according to the gradient of the parameterization energy function, and the key isoparametric surfaces are used as the position constraints of the vertices of the patches of the base complex to optimize the whole hex mesh. The experimental results show that the scaled Jacobian value of hex meshes can be effectively improved by the proposed method.