Abstract
This work presents methods for deforming meshes in a shape-sensitive way using Moving Least Squares (MLS) optimization. It extends an approach for deforming space (Cuno et al. in Proceedings of the 27th Computer Graphics International Conference, pp. 115–122, 2007) by showing how custom distance metrics may be used to achieve deformations which preserve the overall mesh shape. Several variant formulations are discussed and demonstrated, including the use of geodesic distances, distances constrained to paths contained in the mesh, the use of skeletons, and a reformulation of the MLS scheme which makes it possible to affect the bending behavior of the deformation. Finally, aspects of the implementation of these techniques in parallel architectures such as GPUs (graphics processing units) are described and compared with CPU-only implementations.
Similar content being viewed by others
References
Alexa, M.: Interactive shape editing. In: ACM SIGGRAPH Courses (2006)
Arun, K.S., Huang, T.S., Blostein, S.D.: Least-squares fitting of two 3-D point sets. IEEE Trans. Pattern Anal. Mach. Intell. 9(5), 698–700 (1987)
Au, O.K.-C., Fu, H., Tai, C.-L., Cohen-Or, D.: Handle-aware isolines for scalable shape editing. ACM Trans. Graph. 26(3), 83 (2007)
Baran, I., Popović, J.: Automatic rigging and animation of 3D characters. ACM Trans. Graph. 26(3), 72 (2007)
Besl, P.J., McKay, N.D.: A method for registration of 3-D shapes. IEEE Trans. Pattern Anal. Mach. Intell. 14(2), 239–258 (1992)
Botsch, M., Kobbelt, L.: Real-time shape editing using radial basis functions. Comput. Graph. Forum 24(3), 611–621 (2005)
Botsch, M., Pauly, M., Wicke, M., Gross, M.: Adaptive space deformations based on rigid cells. Comput. Graph. Forum 26(3), 339–347 (2007)
Botsch, M., Sorkine, O.: On linear variational surface deformation methods. IEEE Trans. Vis. Comput. Graph. 14(1), 213–230 (2008)
Buck, I., Foley, T., Horn, D., Sugerman, J., Fatahalian, K., Houston, M., Hanrahan, P.: Brook for GPUs: stream computing on graphics hardware. ACM Trans. Graph. 23(3), 777–786 (2004)
Cornea, N.D., Min, P.: Curve-skeleton properties, applications, and algorithms. IEEE Trans. Vis. Comput. Graph. 13(3), 530–548 (2007)
Cuno, A., Esperanca, C., Oliveira, A., Cavalcanti, P.R.: 3D as-rigid-as-possible deformations using MLS. In: Proceedings of the 27th Computer Graphics International Conference, Petropolis, RJ, Brazil, May 2007, pp. 115–122
Fedor, M.: Application of inverse kinematics for skeleton manipulation in real-time. In: SCCG ’03: Proceedings of the 19th Spring Conference on Computer Graphics, New York, NY, USA, pp. 203–212. ACM, New York (2003)
Fu, H., Au, O.K.-C., Tai, C.-L.: Effective derivation of similarity transformations for implicit Laplacian mesh editing. Comput. Graph. Forum 26(1), 34–45 (2007)
Horn, B.K.P.: Closed-form solutions of absolute orientation using unit quaternions. J. Opt. Soc. Am. 4(4), 629–642 (1987)
Kanatani, K.: Analysis of 3-D rotation fitting. IEEE Trans. Pattern Anal. Mach. Intell. 16(5), 543–549 (1994)
Lawrence Livermore National Laboratory: POSIX Threads Programming (1995). https://computing.llnl.gov/tutorials/pthreads/
McCool, M., Du Toit, S., Popa, T., Chan, B., Moule, K.: Shader algebra. ACM Trans. Graph. 23(3), 787–795 (2004)
McCool, M.D., D’Amora, B.: Programming using Rapidmind on the cell BE. In: Proceedings of the ACM/IEEE Conference on Supercomputing, NY, USA, p. 222. ACM, New York (2006)
Nealen, A., Sorkine, O., Alexa, M., Cohen-Or, D.: A sketch-based interface for detail-preserving mesh editing. ACM Trans. Graph. 24(3), 1142–1147 (2005)
NVIDIA Corporation: CUDA Environment—Compute Unified Device Architecture (2007). http://www.nvidia.com/object/cuda_home.html
O’Rourke, J.: Art Gallery Theorems and Algorithms. Oxford University Press, New York (1987)
Owens, J.D., Houston, M., Luebke, D., Green, S., Stone, J.E., Phillips, J.C.: GPU computing. Proc. IEEE 96(5), 879–899 (2008)
Papakipos, M.: The peakstream platform: High-productivity software development for GPUs. In: Proceedings of LCI Conference on High-Performance Clustered Computing (2007)
Schaefer, S., McPhail, T., Warren, J.: Image deformation using moving least squares. ACM Trans. Graph. 25(3), 533–540 (2006)
Sorkine, O., Alexa, M.: As-rigid-as-possible surface modeling. In: SGP’ 07: Proceedings of the Fifth Eurographics Symposium on Geometry Processing, pp. 109–116. Eurographics Association, Aire-la-Ville (2007)
Sumner, R.W., Schmid, J., Pauly, M.: Embedded deformation for shape manipulation. ACM Trans. Graph. 26(3), 80:1–80:7 (2007)
Tarditi, D., Puri, S., Oglesby, J.: Accelerator: using data parallelism to program GPUs for general-purpose uses. In: XII ASPLOS, New York, NY, USA, pp. 325–335. ACM, New York (2006)
Walker, M.W., Shao, L., Volz, R.A.: Estimating 3-D location parameters using dual number quaternions. CVGIP: Image Underst. 54(3), 358–367 (1991)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Cuno Parari, A.E., Esperança, C. & Oliveira, A.A.F. Shape-sensitive MLS deformation. Vis Comput 25, 911–922 (2009). https://doi.org/10.1007/s00371-009-0369-6
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00371-009-0369-6