Character articulation through profile curves

Abstract

Computer animation relies heavily on rigging setups that articulate character surfaces through a broad range of poses. Although many deformation strategies have been proposed over the years, constructing character rigs is still a cumbersome process that involves repetitive authoring of point weights and corrective sculpts with limited and indirect shaping controls. This paper presents a new approach for character articulation that produces detail-preserving deformations fully controlled by 3D curves that profile the deforming surface. Our method starts with a spline-based rigging system in which artists can draw and articulate sparse curvenets that describe surface profiles. By analyzing the layout of the rigged curvenets, we quantify the deformation along each curve side independent of the mesh connectivity, thus separating the articulation controllers from the underlying surface representation. To propagate the curvenet articulation over the character surface, we formulate a deformation optimization that reconstructs surface details while conforming to the rigged curvenets. In this process, we introduce a cut-cell algorithm that binds the curvenet to the surface mesh by cutting mesh elements into smaller polygons possibly with cracks, and then derive a cut-aware numerical discretization that provides harmonic interpolations with curve discontinuities. We demonstrate the expressiveness and flexibility of our method using a series of animation clips.

References

1. E. Benvenuti, A. Chiozzi, G. Manzini, and N. Sukumar. 2019. Extended virtual element method for the Laplace problem with singularities and discontinuities. Computer Methods in Applied Mechanics and Engineering 356 (2019), 571--597.
2. M. Berger. 2017. Chapter 1 - Cut Cells: Meshes and Solvers. In Handbook of Numerical Methods for Hyperbolic Problems, R. Abgrall and C.-W. Shu (Eds.). Handbook of Numerical Analysis, Vol. 18. Elsevier, 1--22.
3. M. Botsch, M. Pauly, M. Gross, and L. Kobbelt. 2006. PriMo: Coupled Prisms for Intuitive Surface Modeling. In Symposium on Geometry Processing. 11--20.
4. M. Botsch and O. Sorkine. 2008. On Linear Variational Surface Deformation Methods. IEEE Transactions on Visualization and Computer Graphics 14, 1 (2008), 213--230.
5. S. Boyé, P. Barla, and G. Guennebaud. 2012. A Vectorial Solver for Free-Form Vector Gradients. ACM Transactions on Graphics 31, 6, Article 173 (2012), 9 pages.
6. E. Burman, S. Claus, P. Hansbo, M. G. Larson, and A. Massing. 2015. CutFEM: Discretizing geometry and partial differential equations. Internat. J. Numer. Methods Engrg. 104, 7 (2015), 472--501.
7. S. Calderon and T. Boubekeur. 2017. Bounding Proxies for Shape Approximation. ACM Transactions on Graphics 36, 4, Article 57 (2017), 13 pages.
8. M. Campen. 2017. Partitioning Surfaces into Quadrilateral Patches: A Survey. In Proc. of the European Association for Computer Graphics: Tutorials. Article 5, 25 pages.
9. Y. Chen, T. A. Davis, W. W. Hager, and S. Rajamanickam. 2008. Algorithm 887: CHOLMOD, Supernodal Sparse Cholesky Factorization and Update/Downdate. ACM Trans. Math. Software 35, 3 (2008), 14 pages.
10. F. de Goes, A. Butts, and M. Desbrun. 2020. Discrete Differential Operators on Polygonal Meshes. ACM Transactions on Graphics 39, 4, Article 110 (2020), 14 pages.
11. F. de Goes, S. Goldenstein, M. Desbrun, and L. Velho. 2011. Exoskeleton: Curve Network Abstraction for 3D Shapes. Computer and Graphics 35, 1 (2011), 112--121.
12. T.-P. Fries and T. Belytschko. 2010. The extended/generalized finite element method: An overview of the method and its applications. Internat. J. Numer. Methods Engrg. 84, 3 (2010), 253--304.
13. R. Gal, O. Sorkine, N. J. Mitra, and D. Cohen-Or. 2009. iWires: An Analyze-and-Edit Approach to Shape Manipulation. ACM Transactions on Graphics 28, 3, Article 33 (2009), 10 pages.
14. G. Gori, A. Sheffer, N. Vining, E. Rosales, N. Carr, and T. Ju. 2017. FlowRep: Descriptive Curve Networks for Free-Form Design Shapes. ACM Transactions on Graphics 36, 4, Article 59 (2017), 14 pages.
15. P. Herholz, T. A. Davis, and M. Alexa. 2017. Localized Solutions of Sparse Linear Systems for Geometry Processing. ACM Transactions on Graphics 36, 6, Article 183 (2017), 8 pages.
16. Z. Huang, N. Carr, and T. Ju. 2019. Variational Implicit Point Set Surfaces. ACM Transactions on Graphics 38, 4, Article 124 (2019), 13 pages.
17. A. Jacobson, I. Baran, L. Kavan, J. Popović, and O. Sorkine. 2012. Fast Automatic Skinning Transformations. ACM Transactions on Graphics 31, 4, Article 77 (2012), 10 pages.
18. A. Jacobson, Z. Deng, L. Kavan, and J.P. Lewis. 2014. Skinning: Real-time Shape Deformation. In ACM SIGGRAPH Courses.
19. P. Joshi, M. Meyer, T. DeRose, B. Green, and T. Sanocki. 2007. Harmonic Coordinates for Character Articulation. ACM Transactions on Graphics 26, 3 (2007), 10 pages.
20. T. Ju, Q.-Y. Zhou, M. van de Panne, D. Cohen-Or, and U. Neumann. 2008. Reusable Skinning Templates Using Cage-Based Deformations. ACM Transactions on Graphics 27, 5, Article 122 (2008), 10 pages.
21. L. Kavan and O. Sorkine. 2012. Elasticity-Inspired Deformers for Character Articulation. ACM Transactions on Graphics 31, 6, Article 196 (2012), 8 pages.
22. B. H. Le and J. P. Lewis. 2019. Direct Delta Mush Skinning and Variants. ACM Transactions on Graphics 38, 4, Article 113 (2019), 13 pages.
23. B. H. Le, K. Villeneuve, and C. Gonzalez-Ochoa. 2021. Direct Delta Mush Skinning Compression with Continuous Examples. ACM Transactions on Graphics 40, 4, Article 72 (2021), 13 pages.
24. J. P. Lewis, M. Cordner, and N. Fong. 2000. Pose Space Deformation: A Unified Approach to Shape Interpolation and Skeleton-Driven Deformation. In Proc. of the 27th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH). 165--172.
25. P. Li, K. Aberman, R. Hanocka, L. Liu, O. Sorkine-Hornung, and B. Chen. 2021. Learning Skeletal Articulations with Neural Blend Shapes. ACM Transactions on Graphics 40, 4 (2021), 1.
26. Y. Lipman, D. Cohen-Or, R. Gal, and D. Levin. 2007. Volume and Shape Preservation via Moving Frame Manipulation. ACM Transactions on Graphics 26, 1 (2007), 14 pages.
27. Y. Lipman, D. Levin, and D. Cohen-Or. 2008. Green Coordinates. ACM Transactions on Graphics 27, 3 (2008), 1--10.
28. Y. Lipman, O. Sorkine, D. Levin, and D. Cohen-Or. 2005. Linear Rotation-invariant Coordinates for Meshes. ACM Transactions on Graphics 24, 3 (2005), 479--487.
29. V. Lucquin, S. Deguy, and T. Boubekeur. 2017. SeamCut: Interactive Mesh Segmentation for Parameterization. In ACM SIGGRAPH 2017 Technical Briefs.
30. J. Mancewicz, M. L. Derksen, H. Rijpkema, and C. A. Wilson. 2014. Delta Mush: Smoothing Deformations While Preserving Detail. In Symposium on Digital Production. 7--11.
31. T. McLaughlin, L. Cutler, and D. Coleman. 2011. Character Rigging, Deformations, and Simulations in Film and Game Production. In ACM SIGGRAPH Courses.
32. N. Moës, J. Dolbow, and T. Belytschko. 1999. A finite element method for crack growth without remeshing. Internat. J. Numer. Methods Engrg. 46, 1 (1999), 131--150.
33. S. E. Mousavi, E. Grinspun, and N. Sukumar. 2011. Harmonic enrichment functions: A unified treatment of multiple, intersecting and branched cracks in the extended finite element method. Internat. J. Numer. Methods Engrg. 85, 10 (2011), 1306--1322.
34. A. Nealen, T. Igarashi, Olga Sorkine, and M. Alexa. 2007. FiberMesh: Designing Freeform Surfaces with 3D Curves. ACM Transactions on Graphics 26, 3, Article 41 (2007).
35. A. Nealen, O. Sorkine, M. Alexa, and D. Cohen-Or. 2005. A Sketch-Based Interface for Detail-Preserving Mesh Editing. ACM Transactions on Graphics 24, 3 (2005), 1142--1147.
36. V. M. Nguyen-Thanh, X. Zhuang, H. Nguyen-Xuan, T. Rabczuk, and P. Wriggers. 2018. A Virtual Element Method for 2D linear elastic fracture analysis. Computer Methods in Applied Mechanics and Engineering 340 (2018), 366--395.
37. A. Orzan, A. Bousseau, P. Barla, H. Winnemöller, J. Thollot, and D. Salesin. 2008. Diffusion Curves: A Vector Representation for Smooth-Shaded Images. ACM Transactions on Graphics 27, 3 (2008), 8 pages.
38. H. Pan, Y. Liu, A. Sheffer, N. Vining, C.-J. Li, and W. Wang. 2015. Flow Aligned Surfacing of Curve Networks. ACM Transactions on Graphics 34, 4, Article 127 (2015), 10 pages.
39. K. Polthier and M. Schmies. 1998. Straightest Geodesics on Polyhedral Surfaces. In Mathematical Visualization: Algorithms, Applications and Numerics. 135--150.
40. S. Schaefer, J. Warren, and D. Zorin. 2004. Lofting Curve Networks Using Subdivision Surfaces. In Symposium on Geometry Processing. 103--114.
41. K. Singh and E. Fiume. 1998. Wires: A Geometric Deformation Technique. In Proc. of the 25th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH). 405--414.
42. O. Sorkine and M. Alexa. 2007. As-Rigid-As-Possible Surface Modeling. In Symposium on Geometry Processing. 109--116.
43. O. Sorkine, D. Cohen-Or, Y. Lipman, M. Alexa, C. Rössl, and H.-P. Seidel. 2004. Laplacian Surface Editing. In Symposium on Geometry Processing. 175--184.
44. O. Stein, A. Jacobson, M. Wardetzky, and E. Grinspun. 2020. A Smoothness Energy without Boundary Distortion for Curved Surfaces. ACM Transactions on Graphics 39, 3, Article 18 (2020), 17 pages.
45. T. Sun, P. Thamjaroenporn, and C. Zheng. 2014. Fast Multipole Representation of Diffusion Curves and Points. ACM Transactions on Graphics 33, 4, Article 53 (2014), 12 pages.
46. K. Takayama, O. Sorkine, A. Nealen, and T. Igarashi. 2010. Volumetric Modeling with Diffusion Surfaces. ACM Transactions on Graphics 29, 6, Article 180 (2010), 8 pages.
47. M. Tao, C. Batty, E. Fiume, and D. I. W. Levin. 2019. Mandoline: Robust Cut-Cell Generation for Arbitrary Triangle Meshes. ACM Transactions on Graphics 38, 6, Article 179 (2019), 17 pages.
48. J.-M. Thiery, P. Memari, and T. Boubekeur. 2018. Mean Value Coordinates for Quad Cages in 3D. ACM Transactions on Graphics 37, 6, Article 229 (2018), 14 pages.
49. R. Vaillant, L. Barthe, G. Guennebaud, M.-P. Cani, D. Rohmer, B. Wyvill, O. Gourmel, and M. Paulin. 2013. Implicit Skinning: Real-Time Skin Deformation with Contact Modeling. ACM Transactions on Graphics 32, 4, Article 125 (2013), 12 pages.
50. R. Vaillant, G. Guennebaud, L. Barthe, B. Wyvill, and M.-P. Cani. 2014. Robust Iso-Surface Tracking for Interactive Character Skinning. ACM Transactions on Graphics 33, 6, Article 189 (2014), 11 pages.
51. W. Wang, B. Jüttler, D. Zheng, and Y. Liu. 2008. Computation of Rotation Minimizing Frames. ACM Transactions on Graphics 27, 1, Article 2 (2008), 18 pages.
52. Y. Wang and J. Solomon. 2021. Fast Quasi-Harmonic Weights for Geometric Data Interpolation. ACM Transactions on Graphics 40, 4, Article 73 (2021), 15 pages.
53. J. Wu, R. Westermann, and C. Dick. 2015. A Survey of Physically Based Simulation of Cuts in Deformable Bodies. Computer Graphics Forum 34, 6 (2015), 161--187.
54. Z. Xu, Y. Zhou, E. Kalogerakis, C. Landreth, and K. Singh. 2020. RigNet: Neural Rigging for Articulated Characters. ACM Transactions on Graphics 39, 4, Article 58 (2020), 14 pages.
55. Y. Yu, K. Zhou, D. Xu, X. Shi, H. Bao, B. Guo, and H.-Y. Shum. 2004. Mesh Editing with Poisson-Based Gradient Field Manipulation. ACM Transactions on Graphics 23, 3 (2004), 644--651.
56. R. Zayer, C. Roessl, Z. Karni, and H.-P. Seidel. 2005. Harmonic Guidance for Surface Deformation. Computer Graphics Forum 24, 3 (2005), 601--609.
57. Q. Zhou, T. Weinkauf, and O. Sorkine. 2011. Feature-Based Mesh Editing. In Proc. Eurographics, Short Papers.

Index Terms

• Computing methodologies

  • Computer graphics

    • Animation