Abstract: We present an algorithm for adaptively generating tetrahedral mesh by constructing the density field of a surface model. A uniform sampled point set is first generated inside the axial bounding box of the surface model. A non-uniform density field is defined according to the surface boundary of the model. Under the control of the density field, the centroidal Voronoi tessellation of the point set is constructed by using iterative method, and the distribution of the point set is optimized adaptively via dynamically adding or deleting points. Taking the points inside the surface model as the insertion points, a tetrahedral mesh is generated with the surface mode being the boundary-constraint condition. The experimental results show that our algorithm can handle a variety of surface models with different complexity of topology and geometry, and can adaptively generate tetrahedral mesh with different density distribution by adjusting the density field. Most of the generated tetrahedral cells are more regular and the overall quality of the mesh is higher. Our algorithm can be used for finite element analysis, dynamic simulation, and so on.

Key words: computational geometry, tetrahedral meshing, density field, centroidal Voronoi tessellation, mesh optimization