Mesh Deformation of Dynamic Smooth Manifolds with Surface Correspondences

Maintaining a moving mesh of a deforming surface is widely studied in various disciplines. However, difficulties arise with requirements of topology changes, homeomorphism between mesh and surface, and guarantees of triangle quality. We propose a mesh deformation algorithm to satisfy the above requirements. We employ the skin surface by Edelsbrunner that approximates objects in fields like computer graphics, molecular modeling and engineering. We complete the general deformation framework by introducing a new mesh point movement and scheduling function to satisfy the requirements.

[1]  Adrian Hilton,et al.  Correspondence labelling for wide-timeframe free-form surface matching , 2007, 2007 IEEE 11th International Conference on Computer Vision.

[2]  Evangelos Kokkevis,et al.  Skinning Characters using Surface Oriented Free-Form Deformations , 2000, Graphics Interface.

[3]  Herbert Edelsbrunner,et al.  Deformable Smooth Surface Design , 1999, Discret. Comput. Geom..

[4]  Ho-Lun Cheng,et al.  Quality Tetrahedral Mesh Generation for Macromolecules , 2006, ISAAC.

[5]  Gert Vegter,et al.  Meshing skin surfaces with certified topology , 2005, Ninth International Conference on Computer Aided Design and Computer Graphics (CAD-CG'05).

[6]  Brian Wyvill,et al.  Introduction to Implicit Surfaces , 1997 .

[7]  Guillermo Sapiro,et al.  Region tracking on level-sets methods , 1999, IEEE Transactions on Medical Imaging.

[8]  Harald Garcke,et al.  A parametric finite element method for fourth order geometric evolution equations , 2007, J. Comput. Phys..

[9]  Ho-Lun Cheng,et al.  Quality mesh generation for molecular skin surfaces using restricted union of balls , 2005, VIS 05. IEEE Visualization, 2005..

[10]  T. Creighton.  Proteins: Structures and molecular principles , 1983 .

[11]  Herbert Edelsbrunner,et al.  Relaxed Scheduling in Dynamic Skin Triangulation , 2002, JCDCG.

[12]  Chao Chen,et al.  Superimposing Voronoi Complexes for Shape Deformation , 2004, ISAAC.

[13]  Lawrence H. Staib,et al.  Shape-based 3D surface correspondence using geodesics and local geometry , 2000, Proceedings IEEE Conference on Computer Vision and Pattern Recognition. CVPR 2000 (Cat. No.PR00662).

[14]  Ho-Lun Cheng,et al.  Dynamic Skin Triangulation , 2001, SODA '01.

[15]  Herbert Edelsbrunner,et al.  Design and analysis of planar shape deformation , 1998, SCG '98.

[16]  Ho-Lun Cheng,et al.  Shape space from deformation , 1998, Proceedings Pacific Graphics '98. Sixth Pacific Conference on Computer Graphics and Applications (Cat. No.98EX208).

[17]  Ho-Lun Cheng,et al.  Approximating polyhedral objects with deformable smooth surfaces , 2008, Comput. Geom..