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@heading(Anisotropic Mesh Generation with Particles)
@heading(CMU-CS-96-134)
@center(@b(Frank Bossen))
@center(May 1996@foot)
@center(FTP: CMU-CS-96-134.ps)
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Many important real-world problems require meshing, that is the
approximation of a given geometry by a set of simpler elements such as
triangles or quadrilaterals in two dimensions, and tetrahedra or
hexahedra in three dimensions. Applications include finite element
analysis and computer graphics. This work focuses on the former.
A physically-based model of interacting "particles" is introduced to
uniformly spread points over a 2-dimensional polygonal domain. The set
of points is triangulated to form a triangle mesh. Delaunay
triangulation is used because it guarantees a low computational cost
and reasonably well-shaped elements. Several particle interaction
(repulsion and attraction) models are investigated ranging from
Gaussian energy potentials to Laplacian smoothing. Particle population
control mechanisms are introduced to make the size of the mesh
elements converge to the desired size.
In most applications spatial mesh adaptivity is desirable. Triangles
should not only adapt in size but also in shape, to better fit the
function to approximate. Computational fluid dynamics simulations
typically require triangles stretched in the direction of the flow. A
metric tensor is introduced to quantify the stretching. The
triangulation procedure is changed to generate "Delaunay" meshes in
the Riemannian space defined by the metric.
This new approach to mesh generation appears quite promising.
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