Adaptive and quality quadrilateral/hexahedral meshing from volumetric data

Abstract

This paper describes an algorithm to extract adaptive and quality quadrilateral/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. Some extracted meshes have been extensively used in finite element simulations.

A computer modeling tool for comparing novel ICD electrode orientations in children and adults

“…Elements within a 5 element thick region surrounding the electrodes were split into smaller elements to allow for a higher local mesh density. 24 Using a lookup table with conductivity values, the segmented label map was transformed into a conductivity map of the torso, whose values were then projected onto the computational mesh by sampling with linear interpolation. Conductivities for the individual tissues were based on values derived from the literature as follows (all in siemens/meter): bowel gas 0.002, connective tissue 0.220, liver 0.150, kidney 0.070, skeletal muscle 0.250, fat 0.050, bone 0.006, lung 0.067, blood 0.700, myocardium 0.250.…”

The receding front method applied to hexahedral mesh generation of exterior domains

“…On the one hand, the standard grid-based methods [7][8][9][10][11] are the only family of hexahedral mesh generation algorithms that are robust and fully automatic. In addition, they generate high-quality meshes in the inner part of the mesh.…”

Surface Smoothing and Quality Improvement of Quadrilateral/Hexahedral Meshes with Geometric Flow

“…The comparison of the three quality criteria (the scaled Jacobian, the condition number and Oddy metric) before/after the quality improvement for quad/hex meshes of the human head ( Figure 12) and Ribosome 30S (Figure 1). DATA 1 -before quality improvement; DATA 2 -after quality improvement using the optimization scheme in [2] [3]; DATA 3 -after quality improvement using the combined geometric flow/optimization-based approach. In [2] [3], an optimization approach was used to improve the quality of quad/hex meshes.…”

“…DATA 1 -before quality improvement; DATA 2 -after quality improvement using the optimization scheme in [2] [3]; DATA 3 -after quality improvement using the combined geometric flow/optimization-based approach. In [2] [3], an optimization approach was used to improve the quality of quad/hex meshes. The goal is to remove all the inverted elements and improve the worst condition number of the Jacobian matrix.…”

“…The dual contouring hexahedral meshing method [1] [2] [3] provides a boundary sign for each vertex and each face of a hexahedron, indicating if it lies on the boundary surface or not. For example, a vertex or a face is on the surface if its boundary sign is 1, while lies inside the volume if its boundary sign is 0.…”