TetGen, a Delaunay-Based Quality Tetrahedral Mesh Generator

2015 ◽  
Vol 41 (2) ◽  
pp. 1-36 ◽  
Author(s):  
Hang Si
Keyword(s):  
Tetrahedral Mesh ◽  
Mesh Generator

scholarly journals Tetrahedral mesh generation for medical imaging

2005 ◽  
Author(s):  
Andriy Fedorov ◽  
Nikos Chrisochoides ◽  
Ron Kikinis ◽  
Simon Warfield
Keyword(s):  
Medical Imaging ◽  
Open Source ◽  
Mesh Generation ◽  
Tetrahedral Mesh ◽  
Deformable Objects ◽  
Mr Images ◽  
Mesh Generator ◽  
Preliminary Results ◽  
Tetrahedral Mesh Generation

We describe the open source implementation of an adaptive tetrahedral mesh generator particularly targeted for non-rigid FEM registration of MR images. While many medical imaging applications require robust mesh generation, there are few codes available. Moreover, most of the practical implementations are commercial. The algorithm we have implemented has been previously evaluated for simulations of highly deformable objects, and the preliminary results show its applicability to the targeted application. The implementation we describe is open source and will be available within Insight Toolkit.

Implementation in ALBERTA of an Automatic Tetrahedral Mesh Generator

2007 ◽  
pp. 325-338 ◽  
Author(s):  
R. Montenegro ◽  
J.M. Cascón ◽  
J.M. Escobar ◽  
E. Rodríguez ◽  
G. Montero
Keyword(s):  
Tetrahedral Mesh ◽  
Mesh Generator

scholarly journals An automated tetrahedral mesh generator for computer simulation in Odontology based on the Delaunay’s algorithm

Exacta ◽  
2009 ◽  
Vol 6 (2) ◽  
pp. 237-244
Author(s):  
Mauro Massayoshi Sakamoto ◽  
José Roberto Cardoso ◽  
José Marcio Machado
Keyword(s):  
Computer Simulation ◽  
Software Package ◽  
Tetrahedral Mesh ◽  
Mesh Generator ◽  
Geometric Models ◽  
Homogeneous Structures ◽  
Mesh Generators

In this work, a software package based on the Delaunay’s algorithm is described. The main feature of this package is the capability in applying discretization in geometric domains of teeth taking into account their complex inner structures and the materials with different hardness. Usually, the mesh generators reported in literature treat molars and other teeth by using simplified geometric models, or even considering the teeth as homogeneous structures.

scholarly journals An automated tetrahedral mesh generator for computer simulation in Odontology based on the Delaunay’s algorithm DOI: 10.5585/exacta.v6i2.1204

Exacta ◽  
2009 ◽  
Vol 6 (2) ◽  
pp. 237-244
Author(s):  
Mauro Massayoshi Sakamoto ◽  
José Roberto Cardoso ◽  
José Marcio Machado
Keyword(s):  
Computer Simulation ◽  
Software Package ◽  
Tetrahedral Mesh ◽  
Mesh Generator ◽  
Geometric Models ◽  
Homogeneous Structures ◽  
Mesh Generators

In this work, a software package based on the Delaunay’s algorithm is described. The main feature of this package is the capability in applying discretization in geometric domains of teeth taking into account their complex inner structures and the materials with different hardness. Usually, the mesh generators reported in literature treat molars and other teeth by using simplified geometric models, or even considering the teeth as homogeneous structures.

scholarly journals Tetrahedra of varying density and their applications

2021 ◽  
Author(s):  
Dennis R. Bukenberger ◽  
Hendrik P. A. Lensch
Keyword(s):  
Tetrahedral Mesh ◽  
Rotational Inertia ◽  
Exact Mass ◽  
Accurate Analysis ◽  
Exact Integration ◽  
Voronoi Cells ◽  
Current State ◽  
Chebyshev Norm ◽  
Exact Calculations ◽  
Vector Matrix

Abstract We propose concepts to utilize basic mathematical principles for computing the exact mass properties of objects with varying densities. For objects given as 3D triangle meshes, the method is analytically accurate and at the same time faster than any established approximation method. Our concept is based on tetrahedra as underlying primitives, which allows for the object’s actual mesh surface to be incorporated in the computation. The density within a tetrahedron is allowed to vary linearly, i.e., arbitrary density fields can be approximated by specifying the density at all vertices of a tetrahedral mesh. Involved integrals are formulated in closed form and can be evaluated by simple, easily parallelized, vector-matrix multiplications. The ability to compute exact masses and centroids for objects of varying density enables novel or more exact solutions to several interesting problems: besides the accurate analysis of objects under given density fields, this includes the synthesis of parameterized density functions for the make-it-stand challenge or manufacturing of objects with controlled rotational inertia. In addition, based on the tetrahedralization of Voronoi cells we introduce a precise method to solve $$L_{2|\infty }$$ L 2 | ∞ Lloyd relaxations by exact integration of the Chebyshev norm. In the context of additive manufacturing research, objects of varying density are a prominent topic. However, current state-of-the-art algorithms are still based on voxelizations, which produce rather crude approximations of masses and mass centers of 3D objects. Many existing frameworks will benefit by replacing approximations with fast and exact calculations. Graphic abstract

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