
Biting Ellipses to Generate Anisotropic Mesh
Li, XiangYang, ShangHua Teng and Alper Ungor
Proceedings, 8th International Meshing Roundtable, South Lake Tahoe, CA, U.S.A., pp.97108, October 1999

INTERNATIONAL MESHING ROUNTABLE

Department of Computer Science,
University of Illinois at UrbanaChampaign,
Urbana, IL 61801
Email: ( xli2 
steng 
ungor ) @cs.uiuc.edu
Abstract
In numerical simulation where the underlying function is strongly directional,
it is desirable to use a mesh that is adaptive both in size and in shape. In
such simulation, a metric tensor is used to quantify the ideal size and
direction locally at each point in the domain, which in turn defines the local
stretching and size of the triangles or quadrilaterals of the mesh. Given a
metric tensor, the anisotropic meshing problem is to construct a good quality
mesh satisfying the metric tensor. We present a new anisotropic meshing method
which is called the ellipse biting method. Our algorithm uses the framework of
advancing front to generate a close to optimal packing of ellipses. We then use
the pDelaunay triangulation of the vertex set to generate the final mesh.
Because it generates an ellipse packing that respects the underlying control
spacing, this new method produce a high quality mesh whose element size and
directionality conform well locally to the given input. As part of this work, we
introduces a set of operations includrng scaling, intersection, and union on
ten.sor metrics. Then operations are used to formally define distance among
metrics and to extend Lipschitz condition and the notion of wellshaped meshes
from isotropic metrics to anisotropic metrics.
See also Biting Spheres in 3D by the same authors.
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