“Character articulation through profile curves” by Goes, Sheffler and Fleischer

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.

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.Google ScholarCross Ref
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.Google Scholar
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.Google Scholar
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.Google ScholarDigital Library
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.Google ScholarDigital Library
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.Google ScholarCross Ref
7. S. Calderon and T. Boubekeur. 2017. Bounding Proxies for Shape Approximation. ACM Transactions on Graphics 36, 4, Article 57 (2017), 13 pages.Google ScholarDigital Library
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.Google ScholarDigital Library
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.Google ScholarDigital Library
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.Google ScholarDigital Library
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.Google ScholarDigital Library
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.Google ScholarCross Ref
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.Google ScholarDigital Library
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.Google ScholarDigital Library
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.Google ScholarDigital Library
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.Google ScholarDigital Library
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.Google ScholarDigital Library
18. A. Jacobson, Z. Deng, L. Kavan, and J.P. Lewis. 2014. Skinning: Real-time Shape Deformation. In ACM SIGGRAPH Courses.Google Scholar
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.Google ScholarDigital Library
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.Google ScholarDigital Library
21. L. Kavan and O. Sorkine. 2012. Elasticity-Inspired Deformers for Character Articulation. ACM Transactions on Graphics 31, 6, Article 196 (2012), 8 pages.Google ScholarDigital Library
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.Google ScholarDigital Library
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.Google ScholarDigital Library
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.Google Scholar
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.Google ScholarDigital Library
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.Google ScholarDigital Library
27. Y. Lipman, D. Levin, and D. Cohen-Or. 2008. Green Coordinates. ACM Transactions on Graphics 27, 3 (2008), 1–10.Google ScholarDigital Library
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.Google ScholarDigital Library
29. V. Lucquin, S. Deguy, and T. Boubekeur. 2017. SeamCut: Interactive Mesh Segmentation for Parameterization. In ACM SIGGRAPH 2017 Technical Briefs.Google Scholar
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.Google Scholar
31. T. McLaughlin, L. Cutler, and D. Coleman. 2011. Character Rigging, Deformations, and Simulations in Film and Game Production. In ACM SIGGRAPH Courses.Google Scholar
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.Google ScholarCross Ref
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.Google Scholar
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).Google ScholarDigital Library
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.Google ScholarDigital Library
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.Google ScholarCross Ref
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.Google ScholarDigital Library
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.Google ScholarDigital Library
39. K. Polthier and M. Schmies. 1998. Straightest Geodesics on Polyhedral Surfaces. In Mathematical Visualization: Algorithms, Applications and Numerics. 135–150.Google Scholar
40. S. Schaefer, J. Warren, and D. Zorin. 2004. Lofting Curve Networks Using Subdivision Surfaces. In Symposium on Geometry Processing. 103–114.Google Scholar
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.Google Scholar
42. O. Sorkine and M. Alexa. 2007. As-Rigid-As-Possible Surface Modeling. In Symposium on Geometry Processing. 109–116.Google Scholar
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.Google Scholar
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.Google ScholarDigital Library
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.Google ScholarDigital Library
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.Google ScholarDigital Library
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.Google ScholarDigital Library
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.Google ScholarDigital Library
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.Google ScholarDigital Library
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.Google ScholarDigital Library
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.Google ScholarDigital Library
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.Google ScholarDigital Library
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.Google ScholarDigital Library
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.Google ScholarDigital Library
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.Google ScholarDigital Library
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.Google ScholarCross Ref
57. Q. Zhou, T. Weinkauf, and O. Sorkine. 2011. Feature-Based Mesh Editing. In Proc. Eurographics, Short Papers.Google Scholar