Robust One-to-One Sweeping with Harmonic S-T Mappings and Cages
Cai, Shengyong and Timothy J. Tautges
22nd International Meshing Roundtable, Springer-Verlag, pp.1-18, October 13-16 2013
22nd International Meshing Roundtable
University of Wisconsin-Madison, Madison, WI, U.S.A.
MCS, Argonne National Laboratory, Madison, WI, U.S.A.
Email: firstname.lastname@example.org, email@example.com
A sweeping algorithm can generate hexahedral meshes 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 the source
surface. The traditional method is to use the affine transformation, like translation,
rotation, scaling or combinations of them. This method works very well
on the convex cases, while it fails for concave and multiply-connected surfaces.
In this paper, harmonic function is used to map meshes from a source surface
to its target surface. The result shows that it can generate an all-quad mesh
on the target surface with good quality without any inverted elements and
thus avoid expensive smoothing algorithm (untangling). In order to generate
interior nodes between the source and target surface, cage-based deformation
method is applied with good mesh quality as well.
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