This paper discusses the problem of subdividing meshes containing tetrahedra, pyramids, prisms or hexahedra into a consistent set of tetrahedra. This problem occurs in computer graphics where meshes with pyramids, prisms or hexahedra must be subdivided into tetrahedra to use efficient algorithms for volume rendering, iso-contouring and particle advection. Another application is for the use of s...

We propose constraint sets as an efficient data structure for topology-changing deformable tetrahedral meshes. Using constraint sets, data structure updates in case of topology changes are simple and efficient. The consistency of the geometric representation is maintained and elasto-mechanical properties of the object are preserved. In combination with a Finite Element model for elasto-plastic ...

A family of continuously differentiable piecewise polynomials of degree 9 and higher, on general tetrahedral grids, is constructed, by simplifying and extending the P9 element of Ženǐsek. A mathematical justification and numerical tests are presented. The current computing power is still limited for the computation with 3D C1 finite elements in general. The construction here mainly serves the p...

This paper addresses fully space-time adaptive magnetic field computations. We describe an adaptive Whitney finite element method for solving the magnetoquasistatic formulation of Maxwell’s equations on unstructured 3D tetrahedral grids. Spatial mesh refinement and coarsening are based on hierarchical error estimators especially designed for combining tetrahedral H(curl)-conforming edge element...

|In this paper, an extension of the previously developed 2-D dynamic bubble system for 3-D automatic mesh generation using tetrahedral nite elements is presented. Initially, set of vertices inside the entire analysis region is generated using 3-D dynamic bubble system, followed by automatic mesh generation according to the Delaunay tessellation algorithm and the generated set of vertices. The p...

We address the problem of performing spatial and topological queries on simplicial and cellular meshes. These arise in several application domains including 3D GIS, scientific visualization and finite element analysis. Firstly, we present a family of spatial indexes for tetrahedral meshes, that we call tetrahedral trees. Then, we present the PRstar octree, that is a combined spatial data struct...

We propose a new strategy for boundary conforming meshing that decouples the problem of building tetrahedra of proper size and shape from the problem of conforming to complex, non-manifold boundaries. This approach is motivated by the observation that while several methods exist for adaptive tetrahedral meshing, they typically have difficulty at geometric boundaries. The proposed strategy avoid...

We define quality differential coordinates (QDC) for per-vertex encoding of the quality of a tetrahedral mesh. QDC measures the deviation of a mesh vertex from a position which maximizes the combined quality of the set of tetrahedra incident at that vertex. Our formulation allows the incorporation of different choices of element quality metrics into QDC construction to penalize badly shaped and...