Edge-Based Quadrilateral Mesh Fitting Using Normal Vector Diffusion

Abstract

Nowadays, many manufacturers use computer-aided design (CAD) for processes such as computer numerical control (CNC) machining, simulations, and press working. They use CAD models for their simulations because the cost of performance simulations is lower than that of actual product testing. In this paper, we consider hexahedral meshes for finite element analysis because simulations using such meshes are more accurate than those using tetrahedral meshes. Our aim is to automatically generate hexahedral meshes with sharp features that precisely represent the corresponding features of the target shape. Our hexahedral mesh generation algorithm is voxel-based, and thus in our previous studies, we fitted the surface of voxels to the target surface using Laplacian energy minimization. We used normal vectors during the fitting to preserve any existing sharp features. Each face of the boundary surface of a hexahedral mesh is a quadrilateral face, which we consider to consist of four triangles. Herein, we assume that an edge of a quadrilateral surface has four normal vectors of four connected triangles. Here, we diffuse normal vectors of the target shape after extracting them to accurately preserve the shape features. Moreover, for the Laplacian energy, we add a term that matches the normal vector of the target shape with the four normal vectors of a boundary edge. Finally, we present some experimental results using our method.