We introduce a new algorithm for generating tetrahedral meshes that conform to physical boundaries in volumetric domains consisting of multiple materials. The proposed method allows for an arbitrary number of materials, produces high-quality tetrahedral meshes with upper and lower bounds on dihedral angles, and guarantees geometric fidelity. Moreover, the method is combinatoric so its implement...

Deformable models are used in many computer graphic and animation applications, such as virtual environments, video games, medical simulations, and engineering analysis. Techniques for simulating deformable objects often require a mesh of discrete, tetrahedral elements that represent the object being modeled. This paper describes the implementation of a fast and robust method to generate a tetr...

This paper addresses the existence and construction of Hamiltonian paths and Hamiltonian cycles on conforming tetrahedral meshes. The paths and cycles are constrained to pass from one tetrahedron to the next one through a vertex. For conforming tetrahedral meshes, under certain conditions which are normally satisfied in finite-element computations, we show that there exists a through-vertex Ham...

This paper describes an algorithm to extract adaptive and quality 3D meshes directly from volumetric imaging data. The extracted tetrahedral and hexahedral 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 ...

This paper describes an algorithm to extract adaptive and quality 3D meshes directly from volumetric imaging data. The extracted tetrahedral and hexahedral meshes are extensively used in the finite element method (FEM). A top-down octree subdivision coupled with a dual contouring method is used to rapidly extract adaptive 3D finite element meshes with correct topology from volumetric imaging da...

We address the problem of performing spatial queries on tetrahedral meshes. These latter arise in several application domains including 3D GIS, scientific visualization, finite element analysis. We have defined and implemented a family of spatial indexes, that we call tetrahedral trees. Tetrahedral trees are based on a subdivision of a cubic domain containing the mesh defined either by an octre...

The finite element method and its application to the simulation of static linear elasticity has a long research history. The same applies for Bernstein–Bézier representations of curves and surfaces in computer aided geometric design. However, the combination of both to build tetrahedral Bernstein–Bézier finite elements presents an inspiring and fruitful challenge. The theory and implementation ...