Tianyun Ni
Jason Mitchell
ABSTRACT
Subdivision surfaces provide a compact representation for smooth surfaces that facilitate modeling and animation. They have widespread application in the movie industry, and there's a natural desire to use them also in real-time applications. This course presents theoretical results, implementations, applications, and future research directions. Topics include an introduction to subdivision surfaces, an overview of the surface-evaluation algorithms that are suitable for real-time rendering, implementation of those algorithms on current and next-generation GPUs, and other practical considerations. The course concludes with a section on practical application of these theoretical schemes and GPU implementations to Valve's source game engine and ILM's film production.
- {AB08} Marc Alexa and Tamy Boubekeur. Subdivision Shading. ACM Trans. Graph, Siggraph Asia, 27(5):142, 2008. Google Scholar
Digital Library
- {BA08} Tamy Boubekeur and Marc Alexa. Phong Tessellation. ACM Trans. Graph, Siggraph Asia, 27(5):141, 2008. Google ScholarDigital Library
- {BBB87} Richard H. Bartels, John C. Beatty, and Brian A. Barsky. An Introduction to Splines for Use in Computer Graphics&Geometric Modeling. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA, 1987. Google ScholarDigital Library
- {Bez77} Pierre E. Bezier. Essai de Definition Numerique des Courbes et des Surfaces Experimentales. Ph.d. thesis, Universite Pierre et Marie Curie, February 1977.Google Scholar
- {BG75} R. Barnhill and J. Gregory. Compatible Smooth Interpolation in Triangles. J of Approx. Theory, 15(3):214--225, 1975.Google ScholarCross Ref
- {BRS05} Tamy Boubekeur, Patrick Reuter, and Christophe Schlick. Scalar Tagged PN Triangles. In EUROGRAPHICS 2005 (Short Papers). Eurographics, 2005.Google Scholar
- {BS02} J. Bolz and P. Schröder. Rapid Evaluation of Catmull-Clark Subdivision Surfaces. In Proceedings of the Web3D 2002 Symposium, pages 11--18. ACM Press, 2002. Google ScholarDigital Library
- {BS05} Tamy Boubekeur and Christophe Schlick. Generic Mesh Refinement on Gpu. In ACM SIGGRAPH/Eurographics Graphics Hardware, 2005. Google ScholarDigital Library
- {BS07} Tamy Boubekeur and Christophe Schlick. QAS: Real-Time Quadratic Approximation of Subdivision Surfaces. In Marc Alexa, Steven J. Gortler, and Tao Ju, editors, Proceedings of the Pacific Conference on Computer Graphics and Applications, Pacific Graphics 2007, Maui, Hawaii, USA, October 29 -- November 2, 2007, pages 453--456. IEEE Computer Society, 2007. Google ScholarDigital Library
- {BS08} Tamy Boubekeur and Christophe Schlick. A Flexible Kernel for Adaptive Mesh Refinement on GPU. Computer Graphics Forum, 27(1):102--114, 2008.Google ScholarCross Ref
- {Bun05} Michael Bunnell. GPU Gems 2: Programming Techniques for High-Performance Graphics and General-Purpose Computation, chapter Adaptive Tessellation of Subdivision Surfaces With Displacement Mapping. Addison-Wesley, Reading, MA, 2005.Google Scholar
- {Cas08a} Ignacio Castaño. Next-Generation Rendering of Subdivision Surfaces, 2008. SIGGRAPH.Google Scholar
- {Cas08b} Ignacio Castaño. Tessellation of Subdivision Surfaces in Directx 11, 2008. Gamefest.Google Scholar
- {CC78} Edwin Catmull and James Clark. Recursively Generated B-Spline Surfaces on Arbitrary Topological Meshes. Computer-Aided Design, pages 350--355, 1978.Google ScholarCross Ref
- {CDM91} A. S. Cavaretta, W. Dahmen, and C. A. Micchelli. Stationary Subdivision. Memoirs of the American Mathematical Society, 93(453):1--186, 1991.Google ScholarCross Ref
- {CH02} Nathan A. Carr and John C. Hart. Meshed Atlases for Real-Time Procedural Solid Texturing. ACM Trans. Graph., 21(2):106--131, 2002. Google ScholarDigital Library
- {CHCH06} Nathan A. Carr, Jared Hoberock, Keenan Crane, and John C. Hart. Rectangular Multi-chart Geometry Images. In SGP '06: Proceedings of the fourth Eurographics symposium on Geometry processing, pages 181--190, Aire-la-Ville, Switzerland, Switzerland, 2006. Eurographics Association. Google ScholarDigital Library
- {COM98} Jonathan Cohen, Marc Olano, and Dinesh Manocha. Appearance-Preserving Simplification. In SIGGRAPH '98: Proceedings of the 25th annual conference on Computer graphics and interactive techniques, pages 115--122, New York, NY, USA, 1998. ACM. Google ScholarDigital Library
- {Coo84} Robert L. Cook. Shade Trees. SIGGRAPH Comput. Graph., 18(3):223--231, 1984. Google ScholarDigital Library
- {dB93} Carl de Boor. On the Evaluation of Box Splines. Numerical Algorithms, 5(1--4):5--23, 1993.Google Scholar
- {DBG+06} Shen Dong, Peer-Timo Bremer, Michael Garland, Valerio Pascucci, and John C. Hart. Spectral Surface Quadrangulation. ACM Trans. Graph., 25(3):1057--1066, 2006. Google ScholarDigital Library
- {Dia08} Rich Diamant. Autodesk Mudbox: Integration and Use with Autodesk 3ds Max and Autodesk Maya. In Game Developer's Conference, 2008.Google Scholar
- {DKT98} T. DeRose, M. Kass, and T. Truong. Subdivision Surfaces in Character Animation. In SIGGRAPH '98: Proceedings of the 25th annual conference on Computer graphics and interactive techniques, pages 85--94, New York, NY, USA, 1998. ACM Press. Google ScholarDigital Library
- {DRS08} C. Dyken, M. Reimers, and J. Seland. Real-Time Gpu Silhouette Refinement Using Adaptively Blended Bezier Patches. In Computer Graphics Forum 27 (1), pages 1--12, 2008.Google Scholar
- {DRSar} Christopher Dyken, Martin Reimers, and Johan Seland. Semi-Uniform Adaptive Patch Tessellation. Computer Graphics Forum, to appear.Google Scholar
- {DS78} D. Doo and M. Sabin. Behaviour of recursive division surfaces near extraordinary points. Computer-Aided Design, 10:356--360, September 1978.Google ScholarCross Ref
- {DWS+88} Michael Deering, Stephanie Winner, Bic Schediwy, Chris Duffy, and Neil Hunt. The Triangle Processor and Normal Vector Shader: a VLSI System for High Performance Graphics. In SIGGRAPH '88: Proceedings of the 15th annual conference on Computer graphics and interactive techniques, pages 21--30, New York, NY, USA, 1988. ACM. Google ScholarDigital Library
- {Far97} Gerald Farin. Curves and Surfaces for Computer-Aided Geometric Design: A Practical Guide. Academic Press, pub-ACADEMIC:adr, fourth edition, 1997.Google Scholar
- {FH05} Michael S. Floater and Kai Hormann. Surface Parameterization: a Tutorial and Survey. pages 157--186, 2005.Google Scholar
- {For03} Tom Forsyth. Practical Displacement Mapping. In Game Developers Conference, 2003.Google Scholar
- {For06} Tom Forsyth. Linear-Speed Vertex Cache Optimization. 2006.Google Scholar
- {Gee08} Kev Gee. DirectX 11 Tessellation. In Microsoft GameFest, 2008.Google Scholar
- {GP99} Carlos Gonzalez and Jörg Peters. Localized Hierarchy Surface Splines. In S. N. Spencer J. Rossignac, editor, ACM Symposium on Interactive 3D Graphics, 1999. Google ScholarDigital Library
- {Gre74} J. A. Gregory. Smooth Interpolation Without Twist Constraints, pages 71--88. Academic Press, 1974.Google ScholarCross Ref
- {GS85} Leonidas Guibas and Jorge Stolfi. Primitives for the Manipulation of General Subdivisions and the Computation of Voronoi Diagrams. ACM Trans. Graph., 4(2):74--123, 1985. Google ScholarDigital Library
- {JH08} Jin Ma Xinguo Liu Leif Kobbelt Hujun Bao Jin Huang, Muyang Zhang. Spectral Quadrangulation with Orientation and Alignment Control. SIGGRAPH Asia, 2008.Google Scholar
- {JLW05} Shuangshuang Jin, Robert R. Lewis, and David West. A Comparison of Algorithms for Vertex Normal Computation. The Visual Computer, 21(1-2):71--82, 2005.Google ScholarDigital Library
- {KMDZ09} Denis Kovacs, Jason Mitchell, Shanon Drone, and Denis Zorin. Real-time Creased Approximate Subdivision Surfaces. In I3D '09: Proceedings of the 2009 Symposium on Interactive 3D Graphics and Games, pages 155--160, New York, NY, USA, 2009. ACM. Google ScholarDigital Library
- {KP07} Kestutis Karčiauskas and Jörg Peters. Concentric Tessellation Maps and Curvature Continuous Guided Surfaces. Computer Aided Geometric Design, 24(2):99--111, Feb 2007. Google ScholarDigital Library
- {KPN1} Kestutis Karčiauskas and Jörg Peters. Guided Spline Surfaces. Computer Aided Geometric Design, pages 1--20, 2009 N1. Google ScholarDigital Library
- {KPR04} K. Karciauskas, J. Peters, and U. Reif. Shape Characterization of Subdivision Surfaces -- Case Studies. Computer-Aided Geometric Design, 21(6):601--614, july 2004. Google ScholarDigital Library
- {KSG03} Vladislav Kraevoy, Alla Sheffer, and Craig Gotsman. Matchmaker: Constructing Constrained Texture Maps. 2003.Google Scholar
- {LB06} Charles Loop and Jim Blinn. Real-time GPU Rendering of Piecewise Algebraic Surfaces. ACM Trans. Graph., 25(3):664--670, 2006. Google ScholarDigital Library
- {Lee06} Matt Lee. Next-Generation Graphics Programming on XBox 360. In Microsoft GameFest, 2006.Google Scholar
- {LMH00} Aaron Lee, Henry Moreton, and Hugues Hoppe. Displaced Subdivision Surfaces. In SIGGRAPH '00: Proceedings of the 27th annual conference on Computer graphics and interactive techniques, pages 85--94, 2000. Google ScholarDigital Library
- {Loo92} Charles Loop. Generalized B-Spline Surfaces of Arbitrary Topological Type. PhD thesis, University of Washington, 1992.Google ScholarDigital Library
- {Loo04} Charles Loop. Second Order Smoothness over Extraordinary Vertices. In Symposium on Geometry Processing, pages 169--178, 2004. Google ScholarDigital Library
- {LS08a} Charles Loop and Scott Schaefer. Approximating Catmull-Clark Subdivision Surfaces with Bicubic Patches. ACM Trans. Graph., 27(1):1--11, 2008. Google ScholarDigital Library
- {LS08b} Charles T. Loop and Scott Schaefer. G
2 Tensor Product Splines Over Extraordinary Vertices. Comput. Graph. Forum, 27(5):1373--1382, 2008.Google ScholarDigital Library
- {LY06} Gang Lin and Thomas P. Y. Yu. An improved vertex caching scheme for 3d mesh rendering. IEEE Transactions on Visualization and Computer Graphics, 12(4):640--648, 2006. Google ScholarDigital Library
- {MHAM08} Jacob Munkberg, Jon Hasselgren, and Tomas Akenine-Mller. Non-Uniform Fractional Tessellation. In ACM SIGGRAPH/Graphics Hardware 2008, 2008. Google ScholarDigital Library
- {Mit07} Martin Mittring. Finding Next Gen: CryEngine 2. In SIGGRAPH '07: ACM SIGGRAPH 2007 courses, pages 97--121, New York, NY, USA, 2007. ACM. Google ScholarDigital Library
- {MKP07} Ashish Myles, Kȩstutis Karčiauskas, and Jörg Peters. Extending Catmull-Clark Subdivision and PCCM with Polar Structures. In PG '07: Proceedings of the 15th Pacific Conference on Computer Graphics and Applications, pages 313--320, Washington, DC, USA, 2007. IEEE Computer Society. Google ScholarDigital Library
- {MNP08} Ashish Myles, Tianyun Ni, and Jörg Peters. Fast Parallel Construction of Smooth Surfaces from Meshes with Tri/Quad/Pent Facets. In Symposium on Geometry Processing, July 2 -- 4, 2008, Copenhagen, Denmark, pages 1--8. Blackwell, 2008. Google ScholarDigital Library
- {Mor01} Henry Moreton. Watertight Tessellation Using Forward Differencing. In HWWS '01: Proceedings of the ACM SIGGRAPH/EUROGRAPHICS workshop on Graphics hardware, pages 25--32, New York, NY, USA, 2001. ACM. Google ScholarDigital Library
- {MP09} Ashish Myles and Jörg Peters. Bi-3 C
2 Polar Subdivision. ACM Transactions on Graphics, 2009. Google ScholarDigital Library
- {My108} Ashish Myles. Curvature-Continuous Bicubic Subdivision Surfaces for Polar Configurations. PhD thesis, University of Florida, December 2008.Google Scholar
- {NYM+08} Tianyun Ni, Young In Yeo, Ashish Myles, Vineet Goel, and Jörg Peters. GPU Smoothing of Quad Meshes. In IEEE International Conference on Shape Modeling and Applications, 2008.Google Scholar
- {PB00} Dan Piponi and George Borshukov. Seamless Texture Mapping of Subdivision Surfaces by Model Pelting and Texture Blending. In SIGGRAPH '00: Proceedings of the 27th annual conference on Computer graphics and interactive techniques, pages 471--478, New York, NY, USA, 2000. ACM Press/Addison-Wesley Publishing Co. Google ScholarDigital Library
- {PBP02} H. Prautzsch, W. Boehm, and M. Paluszny. Bézier and B-Spline Techniques. Mathematics and Visualization. Springer-Verlag, Berlin, 2002. Google ScholarDigital Library
- {PCK04} Budirijanto Purnomo, Jonathan D. Cohen, and Subodh Kumar. Seamless Texture Atlases. In SGP '04: Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing, pages 65--74, New York, NY, USA, 2004. ACM. Google ScholarDigital Library
- {Pet91} Jörg Peters. Smooth Interpolation of a Mesh of Curves. Constructive Approximation, 7:221--247, 1991. Winner of SIAM Student Paper Competition 1989.Google ScholarCross Ref
- {Pet95} Jörg Peters. C
1-Surface Splines. SIAM Journal on Numerical Analysis, 32(2):645--666, 1995. Google ScholarDigital Library
- {Pet02} Jörg Peters. Geometric Continuity. In Handbook of Computer Aided Geometric Design, pages 193--229. Elsevier, 2002.Google ScholarCross Ref
- {Pet04} Jörg Peters. Mid-Structures of Subdividable Linear Efficient Function Enclosures Linking Curved and Linear Geometry. In Miriam Lucian and Marian Neamtu, editors, Proceedings of SIAM conference, Seattle, Nov 2003. Nashboro, 2004.Google Scholar
- {Pet08} Jörg Peters. PN-Quads. Technical Report 2008-421, Dept CISE, University of Florida, 2008.Google Scholar
- {PK09} Jörg Peters and K. Karčiauskas. An introduction to guided and polar surfacing. In Mathematics of Curves and Surfaces, pages 1--26, 2009. Seventh International Conference on Mathematical Methods for Curves and Surfaces Toensberg, Norway.Google Scholar
- {PR98} J. Peters and U. Reif. The 42 Equivalence Classes of Quadratic Surfaces in Affine N-Space. Computer-Aided Geometric Design, 15:459--473, 1998.Google ScholarCross Ref
- {PR08} J. Peters and U. Reif. Subdivision Surfaces, volume 3 of Geometry and Computing. Springer-Verlag, New York, 2008. Google ScholarDigital Library
- {PT97} Les Piegl and Wayne Tiller. The NURBS Book (2nd ed.). Springer-Verlag New York, Inc., New York, NY, USA, 1997. Google ScholarDigital Library
- {PW08} J. Peters and X. Wu. Net-to-Surface Distance of Subdivision Functions. JAT, page xx, 2008. in press.Google Scholar
- {SAUK04} Le-Jeng Shiue, Pierre Alliez, Radu Ursu, and Lutz Kettner. A Tutorial on CGAL Polyhedron for Subdivision Algorithms. In 2nd CGAL User Workshop, 2004. http://www.cgal.org/Tutorials/Polyhedron/.Google Scholar
- {SJP05} Le-Jeng Shiue, Ian Jones, and J. Peters. A Realtime GPU Subdivision Kernel. In Marcus Gross, editor, Siggraph 2005, Computer Graphics Proceedings, Annual Conference Series, pages 1010--1015. ACM Press / ACM SIGGRAPH / Addison Wesley Longman, 2005. Google ScholarDigital Library
- {SNB07} Pedro V. Sander, Diego Nehab, and Joshua Barczak. Fast Triangle Reordering for Vertex Locality and Reduced Overdraw. ACM Trans. Graph., 26(3):89, 2007. Google ScholarDigital Library
- {SPR06} Alla Sheffer, Emil Praun, and Kenneth Rose. Mesh Parameterization Methods and Their Applications. Found. Trends. Comput. Graph. Vis., 2(2):105--171, 2006. Google ScholarDigital Library
- {SSRS74} Ivan E. Sutherland, Robert F. Sproull, Robert, and A. Schumacker. A Characterization of Ten Hidden-Surface Algorithms. ACM Computing Surveys, 6:1--55, 1974. Google ScholarDigital Library
- {ST90} Takafumi Saito and Tokiichiro Takahashi. Comprehensible Rendering of 3D Shapes. SIGGRAPH Comput. Graph., 24(4):197--206, 1990. Google ScholarDigital Library
- {Sta98} Jos Stam. Exact Evaluation of Catmull-Clark Subdivision Surfaces at Arbitrary Parameter Values. In M. Cohen, editor, SIGGRAPH 98 Proceedings, pages 395--404. Addison Wesley, 1998. Google ScholarDigital Library
- {SW07} S. Schaefer and J. Warren. Exact Evaluation of Non-Polynomial Subdivision Schemes at Rational Parameter Values. In PG '07: 15th Pacific Conference on Computer Graphics and Applications, pages 321--330, Los Alamitos, CA, USA, 2007. IEEE Computer Society. Google ScholarDigital Library
- {SZBN03} Thomas W. Sederberg, Jianmin Zheng, Almaz Bakenov, and Ahmad Nasri. T-splines and T-NURCCs. In Jessica Hodgins and John C. Hart, editors, Proceedings of ACM SIGGRAPH 2003, volume 22(3) of ACM Transactions on Graphics, pages 477--484. ACM Press, 2003. Google ScholarDigital Library
- {TACSD06} Y. Tong, P. Alliez, D. Cohen-Steiner, and M. Desbrun. Designing Quadrangulations with Discrete Harmonic Forms. Eurographics Symposium on Geometry Processing, 2006. Google ScholarDigital Library
- {Tat07} Natasha Tatarchuk. Real-Time Tessellation on the GPU. In SIGGRAPH Advanced Real-Time Rendering in 3D Graphics and Games Course, 2007.Google Scholar
- {Tat08} Andrei Tatarinov. Instanced Tessellation in Directx 10, 2008. GDC, http://developer.nvidia.com/object/gamefest-2008-subdiv.html.Google Scholar
- {Va107} Michal Valient. Deferred Rendering in Killzone 2. In DEVELOP Conference, Brighton, UK, 2007.Google Scholar
- {VPBM01} Alex Vlachos, Jörg Peters, Chas Boyd, and Jason Mitchell. Curved PN Triangles. In I3D 2001: Proceedings of the 2001 Symposium on Interactive 3D Graphics, pages 159--166, 2001. Google ScholarDigital Library
- {vW86} J. van Wijk. Bicubic Patches for Approximating Non-Rectangular Control-Point Meshes. Computer Aided Geometric Design, 3(1):1--13, 1986. Google ScholarDigital Library
- {WP04} X. Wu and J. Peters. Interference Detection for Subdivision Surfaces. Computer Graphics Forum, Eurographics 2004, 23(3):577--585, 2004.Google Scholar
- {WP05} X. Wu and J. Peters. An Accurate Error Measure for Adaptive Subdivision surfaces. In Proceedings of The International Conference on Shape Modeling and Applications 2005, pages 51--57, 2005. Google ScholarDigital Library
- {WW02} J. Warren and H. Weimer. Subdivision Methods for Geometric Design. Morgan Kaufmann, New York, 2002. Google ScholarDigital Library
- {YNM+} Young In Yeo, Tianyun Ni, Ashish Myles, Vineet Goel, and Jörg Peters. Parallel Smoothing of Quad Meshes. The Visual Computer, pages x--x. accepted, in press, TVCJ-267.Google Scholar
- {ZH97} Hansong Zhang and Kenneth E. Hoff, III. Fast Backface Culling Using Normal Masks. In SI3D '97: Proceedings of the 1997 symposium on Interactive 3D graphics, pages 103--ff., New York, NY, USA, 1997. ACM. Google ScholarDigital Library
- {ZS00} Denis Zorin and Peter Schröder, editors. Subdivision for Modeling and Animation, Course Notes. ACM SIGGRAPH, 2000.Google Scholar
Index Terms
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