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An Analytical Framework for Quadrilateral Surface Mesh Improvement with an Underlying Triangulated Surface Definition

Kiran Shivanna, Nicole Grosland, and Vincent Magnotta

Proceedings, 19th International Meshing Roundtable, Springer-Verlag, pp.85-102, October 3-6 2010

INTERNATIONAL
MESHING
ROUNTABLE

19th International Meshing Roundtable
Chattanooga, Tennessee, USA.
October 3-6, 2010

Center for Computer Aided Design, The University of Iowa.kiran-shivanna@uiowa.edu
Department of Biomedical Engineering, The University of Iowa.nicole-grosland@uiowa.edu
Department of Radiology, The University of Iowa.vincent-magnotta@uiowa.edu

Summary
Surface mesh quality plays a very important role in the solu- tion accuracy and in the quality of the ensuing volumetric mesh. Amongst the techniques available, optimization based methods are commonly used for mesh quality improvement. Optimization methods for volumetric and planar surface mesh quality improvement are very well researched. However, this is not true for non-planar meshes. In this manuscript, we focus on quadrilat- eral non-planar surface meshes obtained during hexahedral mesh generation of anatomic structures. A modi ed untangling function based on node nor- mals for quadrilateral elements is proposed. A parameterization-based method available is enhanced by giving it an analytical framework. A new projection- based method is proposed and its performance is comparable to the parametric method. The results of the enhanced/proposed methods are superior to the results obtained from Laplacian smoothing.

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