Poisson Shape Interpolation

Dong Xu, Hongxin Zhang, Qing Wang, Hujun Bao

State Key Lab. of CAD&CG, Zhejiang University

Abstract

In this paper, we propose a novel shape interpolation approach based on Poisson equation. We formulate the trajectory problem of shape interpolation as solving Poisson equations defined on a domain mesh. A non-linear gradient field interpolation method is proposed to take both vertex coordinates and surface orientation into account. With proper boundary conditions, the in-between shapes are reconstructed implicitly from the interpolated gradient fields, while traditional methods usually manipulate vertex coordinates directly. Besides of global shape interpolation, our method is also applicable to local shape interpolation, and can be further enhanced by incorporating with deformation. Our approach can generate visual pleasing and physical plausible morphing sequences with stable area and volume changes. Experimental results demonstrate that our technique can avoid the shrinkage problem appeared in linear shape interpolation.

Results

Figure 1: Fandisk --> Cube. Note sharp features are preserved.

Figure 2: Bunny --> Rabbit. Note the natural gluing of ears and the rotation of
the head and the tail.

Figure 3: Morphing between human bodies.

Figure 4: Local morphing comparison. The top row is our results,
while the bottom row are results produced by Alexa 2003.

Figure 5: Morphing among three head models. Note these models are not aligned,
and our method can automatically produce rotation effect during morphing.

Figure 6: Incorporating deformation into morphing sequence.
The top row is the original morphing sequence.
The middle row is results with 50% deformation propagated.
The bottom row is results with 100% deformation propagated.

Papers and Talks

Dong Xu, Hongxin Zhang, Qing Wang, Hujun Bao. Poisson Shape Interpolation. ACM Symposium on Solid and Physical Modeling, 2005. [Movie (6MB)][PPT (20MB)]　

Acknowledgements

We wish to thank Dr. Kun Zhou and anonymous reviewers for their helpful discussions, Dr. Zhongding Jiang and Mr. Hongbo Fu for careful proof-reading. Thanks to Mr. Ran Zhou and Mr. Lu Chen for their helping in video production. Models are courtesy of Cyberware, Stanford University and Max-Planck-Institut fur Informatik. This project is supported in partial by NSFC under Grant No.60021201 and No.60033010, and 973 Program of China under Grant No.2002CB312104.

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