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Eigen deformation of 3D models

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Abstract

Recent advances in mesh deformations have been dominated by two techniques: one uses an intermediate structure like a cage which transfers the user intended moves to the mesh, the other lets the user to impart the moves to the mesh directly. The former one lets the user deform the model in real-time and also preserve the shape with sophisticated techniques like Green Coordinates. The direct techniques on the other hand free the user from the burden of creating an appropriate cage though they take more computing time to solve larger non-linear optimizations. It would be ideal to develop a cage-free technique that provides real-time deformation while respecting the local geometry. Using a simple eigen-framework, we devise such a technique. Our framework creates an implicit skeleton automatically. The user only specifies the motion in a simple and intuitive manner, and our algorithm computes a deformation whose quality is similar to that of the cage-based scheme with Green Coordinates.

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Notes

  1. The concept of eigenskeletons is not new and has been used for mesh compression in [17]. For more applications, please refer to the survey papers [20, 34].

  2. In the ideal case, the Laplace–Beltrami operator is symmetric, which makes its eigenvectors orthonormal, and Φ the identity matrix. However, we use area weights when building the Laplace–Beltrami operator, which makes it asymmetric, and Φ a matrix with non-zero off diagonal entries.

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Acknowledgements

We would like to thank the anonymous reviewers for their comments, and also the authors of [26] for providing the software implementation of their work. Meshes used in this paper were obtained from AIM@Shape Shape Repository. This work is supported by the National Science Foundation Grants CCF-0830467 and CCF-0747082.

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  1. Department of Computer Science and Engineering, The Ohio State University, Columbus, OH, USA

    Tamal K. Dey, Pawas Ranjan & Yusu Wang

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  1. Tamal K. Dey
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  2. Pawas Ranjan
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  3. Yusu Wang
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Correspondence to Pawas Ranjan.

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Dey, T.K., Ranjan, P. & Wang, Y. Eigen deformation of 3D models. Vis Comput 28, 585–595 (2012). https://doi.org/10.1007/s00371-012-0705-0

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