Animation space: A truly linear framework for character animation

ABSTRACT

Skeletal subspace deformation (SSD), a simple method of character animation used in many applications, has several shortcomings; the best-known being that joints tend to collapse when bent. We present animation space, a generalization of SSD that greatly reduces these effects and effectively eliminates them for joints that do not have an unusually large range of motion.While other, more expensive generalizations exist, ours is unique in expressing the animation process as a simple linear transformation of the input coordinates. We show that linearity can be used to derive a measure of average distance (across the space of poses), and apply this to improving parametrizations.Linearity also makes it possible to fit a model to a set of examples using least-squares methods. The extra generality in animation space allows for a good fit to realistic data, and overfitting can be controlled to allow fitted models to generalize to new poses. Despite the extra vertex attributes, it is possible to render these animation-space models in hardware with no loss of performance relative to SSD.

REFERENCES

• 1: Marc Alexa, Linear combination of transformations, Proceedings of the 29th annual conference on Computer graphics and interactive techniques, July 23-26, 2002, San Antonio, Texas
• 2: Dragomir Anguelov , Daphne Koller , Hoi-Cheung Pang , Praveen Srinivasan , Sebastian Thrun, Recovering articulated object models from 3D range data, Proceedings of the 20th conference on Uncertainty in artificial intelligence, p.18-26, July 07-11, 2004, Banff, Canada
• 3: Anguelov, D., Srinivasan, P., Koller, D., Thrun, S., Pang, H., and Davis, J. 2004. The correlated correspondence algorithm for unsupervised registration of nonrigid surfaces. In Proceedings of the Neural Information Processing Systems (NIPS) Conference.
• 4: Collins, G. and Hilton, A. 2001. Modelling for character animation. Softw. Focus 2, 2, 44--51.
• 5: Dominé, S. 2003. Mesh skinning. NVIDIA presentation. http://developer.nvidia.com/object/skinning.html.
• 6: Matthias Eck , Tony DeRose , Tom Duchamp , Hugues Hoppe , Michael Lounsbery , Werner Stuetzle, Multiresolution analysis of arbitrary meshes, Proceedings of the 22nd annual conference on Computer graphics and interactive techniques, p.173-182, September 1995 [doi>10.1145/218380.218440]
• 7: Floater, M. S. and Hormann, K. 2004. Surface parameterization: A tutorial and survey. In Multiresolution in Geometric Modelling. N. A. Dodgson et al. eds. Springer-Verlag, New York.
• 8: Gene H. Golub , Charles F. Van Loan, Matrix computations (3rd ed.), Johns Hopkins University Press, Baltimore, MD, 1996
• 9: Doug L. James , Christopher D. Twigg, Skinning mesh animations, ACM Transactions on Graphics (TOG), v.24 n.3, July 2005
• 10: Ladislav Kavan , Jiří Žára, Spherical blend skinning: a real-time deformation of articulated models, Proceedings of the 2005 symposium on Interactive 3D graphics and games, April 03-06, 2005, Washington, District of Columbia [doi>10.1145/1053427.1053429]
• 11: Paul G. Kry , Doug L. James , Dinesh K. Pai, EigenSkin: real time large deformation character skinning in hardware, Proceedings of the 2002 ACM SIGGRAPH/Eurographics symposium on Computer animation, July 21-22, 2002, San Antonio, Texas [doi>10.1145/545261.545286]
• 12: Bruno Lévy , Sylvain Petitjean , Nicolas Ray , Jérome Maillot, Least squares conformal maps for automatic texture atlas generation, Proceedings of the 29th annual conference on Computer graphics and interactive techniques, July 23-26, 2002, San Antonio, Texas
• 13: J. P. Lewis , Matt Cordner , Nickson Fong, Pose space deformation: a unified approach to shape interpolation and skeleton-driven deformation, Proceedings of the 27th annual conference on Computer graphics and interactive techniques, p.165-172, July 2000 [doi>10.1145/344779.344862]
• 14: Nadia Magnenat Thalmann , Frederic Cordier , Hyewon Seo , George Papagianakis, Modeling of Bodies and Clothes for Virtual Environments, Proceedings of the 2004 International Conference on Cyberworlds (CW'04), p.201-208, November 18-20, 2004 [doi>10.1109/CW.2004.47]
• 15: N. Magnenat-Thalmann , R. Laperrière , D. Thalmann, Joint-dependent local deformations for hand animation and object grasping, Proceedings on Graphics interface '88, p.26-33, December 1989, Edmonton, Alberta, Canada
• 16: Alex Mohr , Michael Gleicher, Building efficient, accurate character skins from examples, ACM Transactions on Graphics (TOG), v.22 n.3, July 2003
• 17: Alex Mohr , Luke Tokheim , Michael Gleicher, Direct manipulation of interactive character skins, Proceedings of the 2003 symposium on Interactive 3D graphics, April 27-30, 2003, Monterey, California [doi>10.1145/641480.641488]
• 18: Christopher C. Paige , Michael A. Saunders, LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares, ACM Transactions on Mathematical Software (TOMS), v.8 n.1, p.43-71, March 1982 [doi>10.1145/355984.355989]
• 19: Nicolas Ray , Bruno Levy, Hierarchical Least Squares Conformal Map, Proceedings of the 11th Pacific Conference on Computer Graphics and Applications, p.263, October 08-10, 2003
• 20: Pedro V. Sander , John Snyder , Steven J. Gortler , Hugues Hoppe, Texture mapping progressive meshes, Proceedings of the 28th annual conference on Computer graphics and interactive techniques, p.409-416, August 2001 [doi>10.1145/383259.383307]
• 21: Peter-Pike J. Sloan , Charles F. Rose, III , Michael F. Cohen, Shape by example, Proceedings of the 2001 symposium on Interactive 3D graphics, p.135-143, March 2001 [doi>10.1145/364338.364382]
• 22: Stewart, D. and Leyk, Z. 1994. Meschach library version 1.2b. http://www.math.uiowa.edu/~dstewart/meschach/README.
• 23: Xiaohuan Corina Wang , Cary Phillips, Multi-weight enveloping: least-squares approximation techniques for skin animation, Proceedings of the 2002 ACM SIGGRAPH/Eurographics symposium on Computer animation, July 21-22, 2002, San Antonio, Texas [doi>10.1145/545261.545283]

INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.3 COMPUTER GRAPHICS
      I.3.7 Three-Dimensional Graphics and Realism
          Subjects: Animation

Additional Classification:
  I. Computing Methodologies
  I.3 COMPUTER GRAPHICS
      I.3.5 Computational Geometry and Object Modeling
          Subjects: Hierarchy and geometric transformations

General Terms:
Algorithms, Theory

Keywords:
Character animation, parametrization, skinning