Boundary/finite element meshing from volumetric data with applications

The main research work during my Ph.D. study is to extract adaptive and quality 2D (triangular or quadrilateral) meshes over isosurfaces and 3D (tetrahedral or hexahedral) meshes with isosurfaces as boundaries directly from volumetric imaging data. The software named LBIE-Mesher (Level Set Boundary Interior and Exterior Mesher) is developed. LBIE-Mesher generates 3D meshes for the volume interior to an isosurface, the volume exterior to an isosurface, or the interval volume between two isosurfaces.; An algorithm has been developed to extract adaptive and quality 3D meshes directly from volumetric imaging data. The extracted tetrahedral meshes are extensively used in the Finite Element Method (FEM). A top-down octree subdivision coupled with the dual contouring method is used to rapidly extract adaptive 3D finite element meshes with correct topology from volumetric imaging data. The edge contraction and smoothing methods are used to improve the mesh quality. The main contribution is extending the dual contouring method to crack-free interval volume 3D meshing with feature sensitive adaptation. Compared to other tetrahedral extraction methods from imaging data, our method generates adaptive and quality 3D meshes without introducing any hanging nodes.; Furthermore, another algorithm has been developed to extract adaptive and quality quadrilateral or hexahedral meshes directly from volumetric data. First, a bottom-up surface topology preserving octree-based algorithm is applied to select a starting octree level. Then the dual contouring method is used to extract a preliminary uniform quad/hex mesh, which is decomposed into finer quads/hexes adaptively without introducing any hanging nodes. The positions of all boundary vertices are recalculated to approximate the boundary surface more accurately. Mesh adaptivity can be controlled by a feature sensitive error function, the regions that users are interested in, or finite element calculation results. Finally, a relaxation based technique is deployed to improve mesh quality. Several demonstration examples are provided from a wide variety of application domains.; An approach has been described to smooth the surface and improve the quality of surface/volume meshes with feature preserved using geometric flow. For triangular and quadrilateral surface meshes, the surface diffusion flow is selected to remove noise by re locating vertices in the normal direction, and the aspect ratio is improved with feature preserved by adjusting vertex positions in the tangent direction. For tetrahedral and hexahedral volume meshes, besides the surface vertex movement in the normal and tangent directions, interior vertices are relocated to improve the aspect ratio. Our method has the properties of noise removal, feature preservation and quality improvement of surface/volume meshes, and it is especially suitable for biomolecular meshes because the surface diffusion flow preserves sphere accurately if the initial surface is close to a sphere. (Abstract shortened by UMI.)...