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Application of Harmonic mapping on One-To-One Sweeping

Cai, Shengyong and Tim Tautges

Research Notes, 21st International Meshing Roundtable, Springer-Verlag, pp.Research Note, October 7-10 2012


21st International Meshing Roundtable
San Jose, CA
October 7-10, 2012

Department of Engineering Physics, University of Wisconsin-Madison, 1500 Engineering Dr, Madison, WI, U.S.A.
MCS, Argonne National Laboratory, 425 ERB, 1500 Engineering Dr, Madi-son, WI, U.S.A.

The sweeping algorithm can generate all-hexahedral mesh by sweeping an all-quad mesh on the source surface to the target surface. For one-to-one sweeping, the most difficult thing is to generate an all-quad mesh on the target surface which has the same mesh connectivity as that of source surface. The traditional method is to use the affine transformations, like translation, rotation, scaling, or combinations of them. This method works very well on the convex cases, while it fails for the concave and non-simply connected cases. In this paper, harmonic mapping is used to map an all-quad mesh onto the target surface. The result shows that it can generate an all-quad mesh on the target surface without any inverted element and avoid expensive smoothing algorithm like untangling.

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