As-rigid-as-possible mesh deformation and its application in hexahedral mesh generation

Authors: Wei Peng, Detang Lu, Tao Huang, Rongwang Yin

Abstract: 
This paper presents an efficient and stable as-rigid-as-possible mesh deformation algorithm for planar shape deformation and hexahedral mesh generation. The deformation algorithm aims to preserve two local geometric properties: scale-invariant intrinsic variables and elastic deformation energy, which are together represented in a quadric energy function. To preserve these properties, the position of each vertex is further adjusted by iteratively minimizing this quadric energy function to meet the position constraint of the controlling points. Experimental results show that the deformation algorithm is efficient, and can obtain physically plausible results, which have the same topology structure with the original mesh. Such a mesh deformation method is useful to project the source surface mesh onto the target surfaces in hexahedral mesh generation based on sweep method, and application results show that the proposed method is feasible to mesh projection not only between similar surface contours but also dissimilar surface contours.

Keywords:
Mesh deformation
Scale-invariant intrinsic variables
Elastic deformation energy
Hexahedral mesh generation
As-rigid-as-possible
Quadric energy function

Published in: Advances Engineering Software  (Volumes 65, November 2013)

Publisher: Elsevier

ISSN Information: 0965-9978

As-rigid-as-possible mesh deformation and its application in hexahedral mesh generation

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