Lecture Notes
For the lecture slides and/or handwriten notes, see the protected area.
Below is further material related to the lectures:
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Transformations (29 and 31 March 2010)
Material on transformations is covered by all standard texts in graphics, robotics, and vision. More specialized books are also available. Some good examples are:
- Edward Angel, Interactive Computer Graphics, 5th Ed., Pearson/Addison-Wesley, 2009
- John Craig, Introduction to Robotics, Mechanics, and Control, 3rd. Ed., Pearson/Addison-Wesley, 2005
- Richard Hartley and Andrew Zisserman, Multiple View Geometry in Computer Vision, 2nd Ed., Cambridge U. Press, 2003
- Michael Penna and Richard Patterson, Projective Geometry and its Applications to Computer Graphics, Prentice Hall, 1986
Some relevant lecture notes from CS348a are here:
See also the Wikipedia articles on Rotation Matrices, Rotation Representations, Euler Angles, and Gimbal Lock.
The Gimbal Lock video shown in class is here (along with many other useful Computer Graphics videos).
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Curve Representations (5 and 7 April 2010)
Some relevant lecture notes from CS348a are here:
See the Wikipedia articles:
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Shape Registration and Matching (14 April 2010)
Some papers:
- S. Umeyama, Least Squares Estimation of Transformation Parameters Between Two Point Sets, IEEE Trans. Pattern Anal. Mach. Intell. 13 (4) (1991) 376–380
- P. J. Besl and N. D. McKay. A Method for Registration of 3-D Shapes. IEEE Tras. Pat. Anal. and Mach. Intel. 14(2), pp 239-256, Feb 1992
- Chen, Y.; Medioni, G., Object Modeling by Registration of Multiple Range Images," Proceedings 1991 IEEE International Conference on Robotics and Automation, pp.2724-2729 vol.3, 9-11 Apr 1991
- H. Pottmann and M. Hofer. Geometry of the Squared Distance Function to Curves and Surfaces. In: H.-C. Hege and K. Polthier, editors, Visualization and Mathematics III, pages 221-242, Springer, 2003
- Mikkel B. Stegmann, David Delgado Gomez. A Brief Introduction to Statistical Shape Analysis. Lecture Notes,
Informatics and Mathematical Modelling, Technical University of Denmark, DTU. 2002
- T.F. Cootes and C.J. Taylor. Statistical Models of Appearance for Medical Image Analysis and Computer Vision, Proc. SPIE Medical Imaging 2001
- Szymon Rusinkiewicz, Marc Levoy. Efficient Variants of the ICP Algorithm. 3DIM 2001: 145-152
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Elementary Differential Geometry of Surfaces, Curvature and Normal Estimation for Point Clouds (19 April 2010)
Some books:
- Guggenheimer, Heinrich (1977). "Chapter 10. Surfaces". Differential Geometry. Dover.
- Spivak, Michael (1999). A Comprehensive Introduction to Differential Geometry (Volume 3). Publish or Perish.
Some papers:
- Niloy J. Mitra, An Nguyen, Leonidas Guibas, Estimating Surface Normals in Noisy Point Cloud Data. International Journal of Computational Geometry and Applications. Volume: 14, Issues: 4-5 (2004) pp. 261-276.
- Stefan Gumhold, Xinlong Wang, Rob MacLeod, Feature Extraction from Point Clouds. Submitted.
- Cazals, F. and Pouget, M. 2003. Estimating Differential Quantities Using Polynomial Fitting of Osculating Jets. In Proceedings of the 2003 Eurographics/ACM SIGGRAPH Symposium on Geometry Processing (Aachen, Germany, June 23 - 25, 2003). ACM International Conference Proceeding Series, vol. 43. Eurographics Association, Aire-la-Ville, Switzerland, 177-187.
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Shape Matching (21 April 2010)
Some papers:
- H. Pottmann and M. Hofer. Geometry of the Squared Distance Function to Curves and Surfaces. In: H.-C. Hege and K. Polthier, editors, Visualization and Mathematics III, pages 221-242, Springer, 2003
- Michael Kazhdan's thesis at Princeton. Shape Representations and Algorithms for 3D Model Retrieval. 2004.
- N. J. Mitra, N. Gelfand, H. Pottmann, and L. Guibas. Registration of Point Cloud Data from a Geometric Optimization Perspective. Eurographics Symposium on Geometry Processing, pp. 23-32, 2004.
- N. Gelfand, N. Mitra, L. Guibas and H. Pottmann. Robust Global Registration. Proc. Eurographics Symp. Geom. Processing, pp. 197-206, 2005.
- Wolfson, H.J. and Rigoutsos, I. Geometric Hashing: an Overview. IEEE Computational Science and Engineering, Volume: 4 , Issue: 4 , Oct.-Dec. 1997 Pages:10 - 21.
- Fischler, M. A. and Bolles, R. C. 1981. Random Sample Consensus: a Paradigm for Model Fitting with Applications to Image Analysis and Automated Cartography. Commun. ACM 24, 6 (Jun. 1981), 381-395.
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Voronoi and Delauanay Diagrams, Distance Functions (26 April 2010)
Some relevant lecture notes from CS268 are here:
Some papers:
- H. Alt and L.J. Guibas. Discrete Geometric Shapes: Matching, Interpolation, and Approximation. In J.-R. Sack, J. Urrutia, editors, Handbook of Computational Geometry, pages 121 - 153. Elsevier Science Publishers B.V. North-Holland, Amsterdam, 1999
- H. Alt and M. Godau. Computing the Fréchet Distance Between two Polygonal Curves. Internat. J. Comput. Geom. Appl., 5:75-91, 1995.
- D. HuttenLocher, G. Klanderman and W. Rucklidge. Comparing Images Using the Hausdorff Distance, IEEE Trans. on Pattern Analysis and Machine Intelligence, vol. 15, no. 9, pp. 850-863, 1993.
- Y. Rubner, C. Tomasi and L. J. Guibas. The Earth Mover's Distance as a Metric for Image Retrieval. International Journal of Computer Vision, 40(2) November 2000, pages 99--121
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Nearest Neighbor Search (28 April 2010)
Some papers:
- The Proximity and Location Chapter by David Mount, from the Handbook of Discrete and Computational Geometry, Second Edition. J. E. Goodman and J. O'Rourke, editors CRC Press LLC, Boca Raton, FL; Second Edition, April 2004.
- Songrit Maneewongvatana, David M. Mount. It's Okay to Be Skinny, If Your Friends Are Fat. Center for Geometric Computing, 4th Annual Workshop on Computational Geometry, University of Maryland, 1999.
A visualization of Kirkpatrick's algorithm: http://www.computational-geometry.org/SoCG-videos/socg03video/
See also the nearest neighbor and similarity search Web page: http://simsearch.yury.name/
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Surface Reconstruction: Density Data (03 May 2010)
Some books and papers:
- W. Lorensen, H. Cline: Marching Cubes: A High Resolution 3D Surface Construction Algorithm, SIGGRAPH '87
- J. Bloomenthal: Polygonisation of Implicit Surfaces. Computer-Aided Geometric Design 5(4), 1988
- Nielson and Hamann, The Asymptotic Decider: Resolving the Ambiguity in Marching Cubes, Proceedings of Visualization '91, pages 83-91
- Foley, van Dam, Feiner, Hughes: Computer Graphics: Principles and Practice, Addison Wesley, 1995
- S. Gibson: Using Distance Maps for Accurate Surface Reconstruction in Sampled Volumes, IEEE Volume Visualization Symposium, 1998
- L. Kobbelt, M. Botsch, U. Schwanecke, H.-P. Seidel: Feature Sensitive Surface Extraction from Volume Data, SIGGRAPH ‘01
- T. Ju, F. Losasso, S. Schaeffer, J. Warren: Dual Contouring of Hermite Data, SIGGRAPH ’02
- S. Plantinga and G. Vegter: Isotopic Meshing of Implicit Surfaces, The Visual Computer 23, 2007
- James Sharman: http://www.exaflop.org/docs/marchcubes/
- Paul Bourke: http://local.wasp.uwa.edu.au/~pbourke/geometry/polygonise/
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Surface Reconstruction: Point Sample Data (05 May 2009)
Some books and papers:
- H. Hoppe, T. DeRose, T. Duchamp, J. McDonald, W. Stuetzle: Surface Reconstruction from Unorganized Points, SIGGRAPH 1992.
- J. Carr, R. Beatson, J. Cherrie, T. Mitchell, W. Fright, B. McCallum, T. Evans: Reconstruction and Representation of 3D Objects with Radial Basis Functions, SIGGRAPH 2001.
- Nina Amenta, Marshall Bern and David Eppstein. The Crust and the Beta-Skeleton: Combinatorial Curve Reconstruction, Graphical Models and Image Processing, 60/2:2, pages 125-135 (1998).
- Nina Amenta, Marsahll Bern and Manolis Kamvysselis. A New Voronoi-Based Surface Reconstruction Algorithm, Siggraph '98, pages 415-421 (1998).
- Nina Amenta, Sunghee Choi and Ravi Kolluri. The Power Crust, Proceedings of 6th ACM Symposium on Solid Modeling, 2001, pages 249-260.
- Tamal Dey. Curve and Surface Reconstruction. Cambridge U. Press, 2007.
The crust applet shown in class:
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Smoothing and Remeshing (10 May 2009)
Some papers:
- G. Taubin: A signal processing approach to fair surface design, SIGGRAPH 1995.
- M. Desbrun, M. Meyer, P. Schr(oder, A. H. Barr: Implicit Fairing of Irregular Meshes using Diffusion and Curvature Flow, SIGGRAPH 1999.
- B. Vallet, B. Levy: Spectral Geometry Processing with Manifold Harmonics, Eurographics 2008.
- P. Alliez, M. Meyer, M. Desbrun: Interactive geometry remeshing, SIGGRAPH 2002.
- P. Alliez, E.C. de Verdiere, O. Devillers, M. Isenburg: Isotropic surface remeshing, SMI 2003.
- P. Alliez, D. Cohen-Steiner, O. Devillers, B. Levy, M. Desbrun: Anisotropic polygonal remeshing, SIGGRAPH 2003.
- M. Botsch, L. Kobbelt: A remeshing approach to multiresolution modeling, SGP 2004...
- P. Alliez, G. Ucelli, C. Gotsman, M. Attene: Recent advances in remeshing of surfaces, STAR Report.
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Topology I, Surfaces (12 May 2010)
A paper and a book:
Wikipedia articles:
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Topology II, Complexes and Homology (17 May 2010)
A book:
Wikipedia articles: