Approximating polyhedral objects with deformable smooth surfaces

We propose a method to approximate a polyhedral object with a deformable smooth surface, namely the t-skin defined by Edelsbrunner for all 00. This construction makes it possible for fully automatic, smooth and robust deformation between two polyhedral objects with different topologies. En route to our results, we also give an approximation of a polyhedral object with a union of balls.

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

[2]  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).

[3]  Gert Vegter,et al.  Approximation by skin surfaces , 2003, SM '03.

[4]  Mariette Yvinec,et al.  Conforming Delaunay triangulations in 3D , 2002, SCG '02.

[5]  Sheung-Hung Poon,et al.  Graded conforming Delaunay tetrahedralization with bounded radius-edge ratio , 2003, SODA '03.

[6]  D. Pedoe,et al.  Geometry, a comprehensive course , 1988 .

[7]  Herbert Edelsbrunner,et al.  The union of balls and its dual shape , 1993, SCG '93.

[8]  Philip M. Hubbard,et al.  Approximating polyhedra with spheres for time-critical collision detection , 1996, TOGS.

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

[10]  Alain Fournier,et al.  Matching and Interpolation of Shapes using Unions of Circles , 1996, Comput. Graph. Forum.

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

[12]  Ariel Shamir,et al.  Feature-sensitive 3D shape matching , 2004, Proceedings Computer Graphics International, 2004..

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

[14]  Ho-Lun Cheng,et al.  Guaranteed quality triangulation of molecular skin surfaces , 2004, IEEE Visualization 2004.

[15]  Nina Amenta,et al.  Accurate and efficient unions of balls , 2000, SCG '00.

[16]  Herbert Edelsbrunner,et al.  Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms , 1988, SCG '88.

[17]  Ho-Lun Cheng,et al.  Subdividing Alpha Complex , 2004, FSTTCS.