Dual Laplacian morphing for triangular meshes

Recently, animations with deforming objects have been frequently used in various computer graphics applications. Morphing of objects is one of the techniques which realize shape transformation between two or more existing objects. In this paper, we present a novel morphing approach for 3D triangular meshes with the same topology. The basic idea of our method is to interpolate the mean curvature flow of the input meshes as the curvature flow Laplacian operator encodes the intrinsic local information of the mesh. The in‐between meshes are recovered from the interpolated mean curvature flow in the dual mesh domain due to the simplicity of the neighborhood structure of dual mesh vertices. Our approach can generate visual pleasing and physical plausible morphing sequences and avoid the shrinkage and kinks appeared in the linear interpolation method. Experimental results are presented to show the applicability and flexibility of our approach. Copyright © 2007 John Wiley & Sons, Ltd.

[1]  Marc Alexa,et al.  Merging polyhedral shapes with scattered features , 1999, Proceedings Shape Modeling International '99. International Conference on Shape Modeling and Applications.

[2]  Hugues Hoppe,et al.  Inter-surface mapping , 2004, ACM Trans. Graph..

[3]  David P. Dobkin,et al.  Multiresolution mesh morphing , 1999, SIGGRAPH.

[4]  Hujun Bao,et al.  Poisson shape interpolation , 2005, SPM '05.

[5]  Kun Zhou,et al.  Mesh editing with poisson-based gradient field manipulation , 2004, ACM Trans. Graph..

[6]  Peter Schröder,et al.  Consistent mesh parameterizations , 2001, SIGGRAPH.

[7]  Alla Sheffer,et al.  Cross-parameterization and compatible remeshing of 3D models , 2004, ACM Trans. Graph..

[8]  Christian Rössl,et al.  Laplacian surface editing , 2004, SGP '04.

[9]  Ari Rappoport,et al.  Shape blending using the star-skeleton representation , 1995, IEEE Computer Graphics and Applications.

[10]  Marc Alexa,et al.  As-rigid-as-possible shape interpolation , 2000, SIGGRAPH.

[11]  Wenping Wang,et al.  Interpolating Polyhedral Models Using Intrinsic Shape Parameters , 1997, Comput. Animat. Virtual Worlds.

[12]  Wayne E. Carlson,et al.  Shape transformation for polyhedral objects , 1992, SIGGRAPH.

[13]  Ligang Liu,et al.  Mesh editing with curvature flow laplacian operator , 2005 .

[14]  Ligang Liu,et al.  Dual Laplacian editing for meshes , 2006, IEEE Transactions on Visualization and Computer Graphics.

[15]  Hongbo Fu,et al.  Morphing with Laplacian coordinates and spatial-temporal texture , 2005 .

[16]  Ligang Liu,et al.  Three-dimensional shape blending: intrinsic solutions to spatial interpolation problems , 1999, Comput. Graph..

[17]  Hans-Christian Hege,et al.  Fast and intuitive generation of geometric shape transitions , 2000, The Visual Computer.

[18]  Marc Alexa,et al.  Recent Advances in Mesh Morphing , 2002, Comput. Graph. Forum.

[19]  Gabriel Taubin,et al.  A signal processing approach to fair surface design , 1995, SIGGRAPH.

[20]  Craig Gotsman,et al.  Intrinsic Morphing of Compatible Triangulations , 2003, Int. J. Shape Model..

[21]  Marc Alexa,et al.  Differential coordinates for local mesh morphing and deformation , 2003, The Visual Computer.

[22]  Mark Meyer,et al.  Implicit fairing of irregular meshes using diffusion and curvature flow , 1999, SIGGRAPH.

[23]  Michela Spagnuolo,et al.  Triangle Mesh Duality: Reconstruction and Smoothing , 2003, IMA Conference on the Mathematics of Surfaces.

[24]  Ligang Liu,et al.  Manifold Parameterization , 2006, Computer Graphics International.

[25]  Alla Sheffer,et al.  Pyramid coordinates for morphing and deformation , 2004, Proceedings. 2nd International Symposium on 3D Data Processing, Visualization and Transmission, 2004. 3DPVT 2004..

[26]  Luiz Velho,et al.  Warping and morphing of graphical objects , 1998 .

[27]  Peisheng Gao,et al.  2-D shape blending: an intrinsic solution to the vertex path problem , 1993, SIGGRAPH.

[28]  Anne Verroust-Blondet,et al.  Three-dimensional metamorphosis: a survey , 1998, The Visual Computer.

[29]  Daniel Cohen-Or,et al.  Least-squares meshes , 2004, Proceedings Shape Modeling Applications, 2004..