Mesh generation for voxel -based objects

Abstract

A new physically-based approach to unstructured mesh generation via Monte-Carlo simulation is proposed. Geometrical objects to be meshed are represented by systems of interacting particles with a given interaction potential. A new way of distributing nodes in complex domains is proposed based on a concept of dynamic equilibrium ensemble, which represents a liquid state of matter. The algorithm is simple, numerically stable and produces uniform node distributions in domains of complex geometries and different dimensions. Well-shaped triangles or tetrahedra can be created by connecting a set of uniformly-spaced nodes. The proposed method has many advantages and potential applications. The new method is applied to the problem of meshing of voxel-based objects. By customizing system potential energy function to reflect surface features, particles can be distributed into desired locations, such as sharp corners and edges. Feature-preserved surface mesh can then be constructed by connecting the node set. A heuristic algorithm using an advancing front approach is proposed to generate triangulated surface meshes on voxel-based objects. The resultant surface meshes do not inherit the anisotropy of the underlying hexagonal grid. However, the important surface features, such as edges and corners may not be preserved in the mesh. To overcome this problem, surface features such as edges, corners need to be detected. A new approach of edge capturing is proposed and demonstrated. The approach is based on a Laplace solver with incomplete Jacobi iterations, and as such is very simple and efficient. This edge capturing approach combined with the mesh generation methods above forms a simple and robust technique of unstructured mesh generation on voxel-based objects. A graphical user interface (GUI) capable of complex geometric design and remote simulation control was implemented. The GUI was used in simulations of large fuel-cell stacks. It enables one to setup, run and monitor simulations remotely through secure shell (SSH2) connections. A voxel-based 3D geometrical modeling module is built along with the GUI. The flexibility of voxel-based geometry representation enables one to use this technique for both geometric design and visualization of volume data.