23 research outputs found
Well-Centered Triangulation
Meshes composed of well-centered simplices have nice orthogonal dual meshes
(the dual Voronoi diagram). This is useful for certain numerical algorithms
that prefer such primal-dual mesh pairs. We prove that well-centered meshes
also have optimality properties and relationships to Delaunay and minmax angle
triangulations. We present an iterative algorithm that seeks to transform a
given triangulation in two or three dimensions into a well-centered one by
minimizing a cost function and moving the interior vertices while keeping the
mesh connectivity and boundary vertices fixed. The cost function is a direct
result of a new characterization of well-centeredness in arbitrary dimensions
that we present. Ours is the first optimization-based heuristic for
well-centeredness, and the first one that applies in both two and three
dimensions. We show the results of applying our algorithm to small and large
two-dimensional meshes, some with a complex boundary, and obtain a
well-centered tetrahedralization of the cube. We also show numerical evidence
that our algorithm preserves gradation and that it improves the maximum and
minimum angles of acute triangulations created by the best known previous
method.Comment: Content has been added to experimental results section. Significant
edits in introduction and in summary of current and previous results. Minor
edits elsewher
Triangulation of Simple 3D Shapes with Well-Centered Tetrahedra
A completely well-centered tetrahedral mesh is a triangulation of a three
dimensional domain in which every tetrahedron and every triangle contains its
circumcenter in its interior. Such meshes have applications in scientific
computing and other fields. We show how to triangulate simple domains using
completely well-centered tetrahedra. The domains we consider here are space,
infinite slab, infinite rectangular prism, cube and regular tetrahedron. We
also demonstrate single tetrahedra with various combinations of the properties
of dihedral acuteness, 2-well-centeredness and 3-well-centeredness.Comment: Accepted at the conference "17th International Meshing Roundtable",
Pittsburgh, Pennsylvania, October 12-15, 2008. Will appear in proceedings of
the conference, published by Springer. For this version, we fixed some typo
Velocity Level Approximation of Pressure Field Contact Patches
Pressure Field Contact (PFC) was recently introduced as a method for detailed
modeling of contact interface regions at rates much faster than
elasticity-theory models, while at the same time predicting essential trends
and capturing rich contact behavior. The PFC model was designed to work in
conjunction with error-controlled integration at the acceleration level.
Therefore a vast majority of existent multibody codes using solvers at the
velocity level cannot incorporate PFC in its original form. In this work we
introduce a discrete in time approximation of PFC making it suitable for use
with existent velocity-level time steppers and enabling execution at real-time
rates. We evaluate the accuracy and performance gains of our approach and
demonstrate its effectiveness in simulating relevant manipulation tasks. The
method is available in open source as part of Drake's Hydroelastic Contact
model.Comment: 8 pages, 10 figures. Supplementary video can be found at
https://youtu.be/AdCnTyqqQP
A Dihedral Acute Triangulation of the Cube
It is shown that there exists a dihedral acute triangulation of the
three-dimensional cube. The method of constructing the acute triangulation is
described, and symmetries of the triangulation are discussed.Comment: Minor edits for journal version. Added some material to the
introductio
Tetrahedral Mesh Improvement, Algorithms and Experiments
111 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2001.The persistent appearance of slivers in large three-dimensional Delaunay meshes has been reported as early as 1985. They persist even after treatment with the Delaunay refinement algorithm. Cheng et al. proposed to remove slivers by assigning real weights to the points and change the Delaunay to the weighted Delaunay mesh. This is referred to as the sliver exudation algorithm. Their theoretical bound on the achieved minimum mesh quality is a constant that is positive but exceedingly small. We perform computational experiments to testify the practical effectiveness of sliver exudation.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD
Tetrahedral Mesh Improvement, Algorithms and Experiments
111 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2001.The persistent appearance of slivers in large three-dimensional Delaunay meshes has been reported as early as 1985. They persist even after treatment with the Delaunay refinement algorithm. Cheng et al. proposed to remove slivers by assigning real weights to the points and change the Delaunay to the weighted Delaunay mesh. This is referred to as the sliver exudation algorithm. Their theoretical bound on the achieved minimum mesh quality is a constant that is positive but exceedingly small. We perform computational experiments to testify the practical effectiveness of sliver exudation.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD