skip to main content
research-article

Local Optimization for Robust Signed Distance Field Collision

Published:04 May 2020Publication History
Skip Abstract Section

Abstract

Signed distance fields (SDFs) are a popular shape representation for collision detection. This is due to their query efficiency, and the ability to provide robust inside/outside information. Although it is straightforward to test points for interpenetration with an SDF, it is not clear how to extend this to continuous surfaces, such as triangle meshes. In this paper, we propose a per-element local optimization to find the closest points between the SDF isosurface and mesh elements. This allows us to generate accurate contact points between sharp point-face pairs, and handle smoothly varying edge-edge contact. We compare three numerical methods for solving the local optimization problem: projected gradient descent, Frank-Wolfe, and golden-section search. Finally, we demonstrate the applicability of our method to a wide range of scenarios including collision of simulated cloth, rigid bodies, and deformable solids.

Skip Supplemental Material Section

Supplemental Material

References

  1. Jérémie Allard, François Faure, Hadrien Courtecuisse, Florent Falipou, Christian Duriez, and Paul G Kry. 2010. Volume contact constraints at arbitrary resolution. ACM Trans. Graph. 29, 4 (2010), 82.Google ScholarGoogle ScholarDigital LibraryDigital Library
  2. Kinjal Basu and Art B Owen. 2015. Low discrepancy constructions in the triangle. SIAM J. Numer. Anal. 53, 2 (2015), 743--761.Google ScholarGoogle ScholarCross RefCross Ref
  3. James F Blinn. 1982. A generalization of algebraic surface drawing. ACM Trans. Graph. 1, 3 (1982), 235--256.Google ScholarGoogle ScholarDigital LibraryDigital Library
  4. Jules Bloomenthal and Brian Wyvill. 1997. Introduction to Implicit Surfaces. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA.Google ScholarGoogle Scholar
  5. Robert Bridson, Ronald Fedkiw, and John Anderson. 2002. Robust Treatment of Collisions, Contact and Friction for Cloth Animation. In Proceedings of the 29th Annual Conference on Computer Graphics and Interactive Techniques (San Antonio, Texas) (SIGGRAPH 02). Association for Computing Machinery, New York, NY, USA, 594--603. https://doi.org/10.1145/566570.566623Google ScholarGoogle ScholarDigital LibraryDigital Library
  6. Sean Curtis, Rasmus Tamstorf, and Dinesh Manocha. 2008. Fast Collision Detection for Deformable Models Using Representative-Triangles. In Proceedings of the 2008 Symposium on Interactive 3D Graphics and Games (Redwood City, California) (I3D '08). Association for Computing Machinery, New York, NY, USA, 61--69. https://doi.org/10.1145/1342250.1342260Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. Christer Ericson. 2004. Real-Time Collision Detection. CRC Press, Inc., USA.Google ScholarGoogle Scholar
  8. Kenny Erleben. 2018. Methodology for Assessing Mesh-Based Contact Point Methods. ACM Transactions on Graphics (TOG) 37, 3 (2018), 39.Google ScholarGoogle ScholarDigital LibraryDigital Library
  9. Susan Fisher and Ming C. Lin. 2001. Deformed Distance Fields for Simulation of Non-Penetrating Flexible Bodies. In Computer Animation and Simulation 2001, Nadia Magnenat-Thalmann and Daniel Thalmann (Eds.). Springer Vienna, Vienna, 99--111.Google ScholarGoogle Scholar
  10. Marguerite Frank and Philip Wolfe. 1956. An algorithm for quadratic programming. Naval research logistics quarterly 3, 1-2 (1956), 95--110.Google ScholarGoogle Scholar
  11. Sarah F. Frisken, Ronald N. Perry, Alyn P. Rockwood, and Thouis R. Jones. 2000. Adaptively Sampled Distance Fields: A General Representation of Shape for Computer Graphics. In Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH '00). ACM Press/Addison-Wesley Publishing Co., USA, 249--254. https://doi.org/10.1145/344779.344899Google ScholarGoogle Scholar
  12. Arnulph Fuhrmann, Gerrit Sobotka, and Clemens Gross. 2003. Distance fields for rapid collision detection in physically based modeling. In International Conference on Computer Graphics and Vision '03. Proceedings. Eurographics, Moscow, Russia.Google ScholarGoogle Scholar
  13. Elmer G Gilbert, Daniel W Johnson, and S Sathiya Keerthi. 1988. A fast procedure for computing the distance between complex objects in three-dimensional space. IEEE Journal on Robotics and Automation 4, 2 (1988), 193--203.Google ScholarGoogle ScholarCross RefCross Ref
  14. Eran Guendelman, Robert Bridson, and Ronald Fedkiw. 2003. Nonconvex Rigid Bodies with Stacking. ACM Trans. Graph. 22, 3 (July 2003), 871--878. https://doi.org/10.1145/882262.882358Google ScholarGoogle ScholarDigital LibraryDigital Library
  15. David Harmon, Etienne Vouga, Rasmus Tamstorf, and Eitan Grinspun. 2008. Robust treatment of simultaneous collisions. ACM Trans. Graph. 27, 3 (2008), 23.Google ScholarGoogle ScholarDigital LibraryDigital Library
  16. John C Hart. 1996. Sphere tracing: A geometric method for the antialiased ray tracing of implicit surfaces. The Visual Computer 12, 10 (1996), 527--545.Google ScholarGoogle Scholar
  17. Reiner Horst and Hoang Tuy. 2013. Global optimization: Deterministic approaches. Springer Science & Business Media, Berlin Heidelberg.Google ScholarGoogle Scholar
  18. Martin Jaggi. 2013. Revisiting Frank-Wolfe: Projection-Free Sparse Convex Optimization. In Proceedings of the 30th International Conference on Machine Learning (Proceedings of Machine Learning Research), Sanjoy Dasgupta and David McAllester (Eds.), Vol. 28. PMLR, Atlanta, Georgia, USA, 427--435.Google ScholarGoogle ScholarDigital LibraryDigital Library
  19. Tero Karras. 2012. Maximizing Parallelism in the Construction of BVHs, Octrees, and k-d Trees. In Proceedings of the Fourth ACM SIGGRAPH/Eurographics Conference on High-Performance Graphics (Paris, France) (EGGH-HPG'12). Eurographics Association, Goslar, DEU, 33--37.Google ScholarGoogle ScholarDigital LibraryDigital Library
  20. Jack Kiefer. 1953. Sequential minimax search for a maximum. Proceedings of the American mathematical society 4, 3 (1953), 502--506.Google ScholarGoogle ScholarCross RefCross Ref
  21. Dan Koschier, Crispin Deul, and Jan Bender. 2016. Hierarchical Hp-Adaptive Signed Distance Fields. In Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation (Zurich, Switzerland) (SCA '16). Eurographics Association, Goslar, DEU, 189--198.Google ScholarGoogle ScholarDigital LibraryDigital Library
  22. Fuchang Liu and Young J Kim. 2013. Exact and adaptive signed distance fields computation for rigid and deformable models on gpus. IEEE transactions on visualization and computer graphics 20, 5 (2013), 714--725.Google ScholarGoogle Scholar
  23. Miles Macklin, Matthias Müller, and Nuttapong Chentanez. 2016. XPBD: Position-Based Simulation of Compliant Constrained Dynamics. In Proceedings of the 9th International Conference on Motion in Games (Burlingame, California) (MIG '16). Association for Computing Machinery, New York, NY, USA, 49--54. https://doi.org/10.1145/2994258.2994272Google ScholarGoogle ScholarDigital LibraryDigital Library
  24. Aleka McAdams, Yongning Zhu, Andrew Selle, Mark Empey, Rasmus Tamstorf, Joseph Teran, and Eftychios Sifakis. 2011. Efficient Elasticity for Character Skinning with Contact and Collisions. ACM Trans. Graph. 30, 4, Article 37 (July 2011), 12 pages. https://doi.org/10.1145/2010324.1964932Google ScholarGoogle ScholarDigital LibraryDigital Library
  25. Nathan Mitchell, Mridul Aanjaneya, Rajsekhar Setaluri, and Eftychios Sifakis. 2015. Non-manifold level sets: A multivalued implicit surface representation with applications to self-collision processing. ACM Trans. Graph. 34, 6 (2015), 247.Google ScholarGoogle ScholarDigital LibraryDigital Library
  26. Adam Moravanszky, Pierre Terdiman, and A Kirmse. 2004. Fast contact reduction for dynamics simulation. Game programming gems 4 (2004), 253--263.Google ScholarGoogle Scholar
  27. Matthias Müller, Bruno Heidelberger, Marcus Hennix, and John Ratcliff. 2007. Position based dynamics. J. Vis. Comun. Image Represent. 18, 2 (April 2007), 109--118.Google ScholarGoogle ScholarDigital LibraryDigital Library
  28. Rahul Narain, Armin Samii, and James F O'Brien. 2012. Adaptive anisotropic remeshing for cloth simulation. ACM Trans. Graph. 31, 6 (2012), 152.Google ScholarGoogle ScholarDigital LibraryDigital Library
  29. Xavier Provot. 1997. Collision and self-collision handling in cloth model dedicated to design garments. In Computer Animation and Simulation '97, Daniel Thalmann and Michiel van de Panne (Eds.). Springer Vienna, Vienna, 177--189.Google ScholarGoogle Scholar
  30. J. B. Rosen. 1960. The Gradient Projection Method for Nonlinear Programming. Part I. Linear Constraints. J. Soc. Indust. Appl. Math. 8, 1 (1960), 181--217.Google ScholarGoogle ScholarCross RefCross Ref
  31. J. B. Rosen. 1961. The Gradient Projection Method for Nonlinear Programming. Part II. Nonlinear Constraints. J. Soc. Indust. Appl. Math. 9, 4 (1961), 514--532.Google ScholarGoogle ScholarCross RefCross Ref
  32. Andrew Selle, Jonathan Su, Geoffrey Irving, and Ronald Fedkiw. 2008. Robust high-resolution cloth using parallelism, history-based collisions, and accurate friction. IEEE transactions on visualization and computer graphics 15, 2 (2008), 339--350.Google ScholarGoogle Scholar
  33. Dario Seyb, Alec Jacobson, Derek Nowrouzezahrai, and Wojciech Jarosz. 2019. Non-linear Sphere Tracing for Rendering Deformed Signed Distance Fields. ACM Trans. Graph. 38, 6, Article 229 (Nov. 2019), 12 pages.Google ScholarGoogle ScholarDigital LibraryDigital Library
  34. Eftychios Sifakis and Jernej Barbic. 2012. FEM Simulation of 3D Deformable Solids: A Practitioner's Guide to Theory, Discretization and Model Reduction. In ACM SIGGRAPH 2012 Courses (Los Angeles, California) (SIGGRAPH '12). Association for Computing Machinery, New York, NY, USA, Article 20, 50 pages. https://doi.org/10.1145/2343483.2343501Google ScholarGoogle ScholarDigital LibraryDigital Library
  35. J. Stam. 2009. Nucleus: Towards a unified dynamics solver for computer graphics. In 2009 11th IEEE International Conference on Computer-Aided Design and Computer Graphics. IEEE, USA, 1--11. https://doi.org/10.1109/CADCG.2009.5246818Google ScholarGoogle ScholarCross RefCross Ref
  36. Matthias Teschner, Stefan Kimmerle, Bruno Heidelberger, Gabriel Zachmann, Laks Raghupathi, Arnulph Fuhrmann, M-P Cani, François Faure, Nadia Magnenat-Thalmann, Wolfgang Strasser, et al. 2005. Collision detection for deformable objects. In Computer graphics forum, Vol. 24. Wiley Online Library, USA, 61--81.Google ScholarGoogle Scholar
  37. Bin Wang, François Faure, and Dinesh K. Pai. 2012. Adaptive Image-based Intersection Volume. ACM Trans. Graph. 31, 4, Article 97 (July 2012), 9 pages.Google ScholarGoogle ScholarDigital LibraryDigital Library
  38. Nicholas J Weidner, Kyle Piddington, David IW Levin, and Shinjiro Sueda. 2018. Eulerian-on-lagrangian cloth simulation. ACM Trans. Graph. 37, 4 (2018), 50.Google ScholarGoogle ScholarDigital LibraryDigital Library
  39. Brian Wyvill, Andrew Guy, and Eric Galin. 1999a. Extending the CSG Tree. Warping, Blending and Boolean Operations in an Implicit Surface Modeling System. Computer Graphics Forum 18, 2 (1999), 149--158. https://doi.org/10.1111/1467--8659.00365Google ScholarGoogle ScholarCross RefCross Ref
  40. Brian Wyvill, Andrew Guy, and Eric Galin. 1999b. Extending The CSG Tree. Warping, Blending and Boolean Operations in an Implicit Surface Modeling System. Comput. Graph. Forum 18 (06 1999), 149--158.Google ScholarGoogle Scholar
  41. Hongyi Xu and Jernej Barbic. 2014. Continuous Collision Detection Between Points and Signed Distance Fields. In Workshop on Virtual Reality Interaction and Physical Simulation, Jan Bender, Christian Duriez, Fabrice Jaillet, and Gabriel Zachmann (Eds.). The Eurographics Association, Bremen, Germany. https://doi.org/10.2312/vriphys.20141218Google ScholarGoogle Scholar
  42. Hongyi Xu, Yili Zhao, and Jernej Barbic. 2014. Implicit multibody penalty-based distributed contact. IEEE Trans. Vis. Comput. Graph. 20, 9 (2014), 1266--1279.Google ScholarGoogle ScholarCross RefCross Ref

Index Terms

  1. Local Optimization for Robust Signed Distance Field Collision

        Recommendations

        Comments

        Login options

        Check if you have access through your login credentials or your institution to get full access on this article.

        Sign in

        Full Access

        PDF Format

        View or Download as a PDF file.

        PDF

        eReader

        View online with eReader.

        eReader
        About Cookies On This Site

        We use cookies to ensure that we give you the best experience on our website.

        Learn more

        Got it!