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Quadrilateral Meshing with Directionality Control through the Packing of Square Cells

Shimada, Kenji, Jia-Huei Liao and Takayuki Itoh

Proceedings, 7th International Meshing Roundtable, Sandia National Lab, pp.61-76, October 1998

INTERNATIONAL
MESHING
ROUNTABLE

7th International Meshing Roundtable
October 26-28, 1998
Dearborn, Michigan, USA

Kenji Shimada,
Mechanical Engineering,
Carnegie Mellon University,
Pittsburgh, PA 15213, U.S.A.
Email: shimada@cmu.edu,
Web: http://ciel.me.cmu.edu/shimada/

JiaHuei Liao,
Mechanical Engineering,
Carnegie Mellon University,
Pittsburgh, PA 15213, U.S.A.
Web: http://www.contrib.andrew.cmu.ed u/~jliao

Takayuki Itoh,
IBM Research, Tokyo Research Laboratory,
1623-14 Shimotsuruma, Yamato, Kanagawa, 242, Japan.

Abstract
This paper proposes a computational method for fully automated quadrilateral meshing. Unlike previous methods, this new scheme can create a quadrilateral mesh whose directionality is precisely controlled. Given as input: (1) a 2D geometric domain, (2) a desired node spacing distribution as a scalar function defined over the domain, and (3) a desired mesh directionality as a vector field defined over the domain, the proposed method first packs square cells closely in the domain. The centers of the squares are then connected by Delaunay triangulation, yielding a triangular mesh topology. The triangular mesh is further converted into a quad-dominant mesh or an all-quad mesh that satisfies the given mesh directionality. Since the closely packed square cells mimic a pattern of Voroni polygons corresponding to a well-shaped graded quadrilateral mesh, the proposed method generates a high quality mesh whose element sizes and mesh directionality conform well to the given input.

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