How can computers be used to acquire, analyze and create 3D shapes? In this course, we learn about some answers to this question, and build the understanding necessary to develop new ones. Topics include 3D shape representations, algorithms for geometric analysis, geometric features and symmetry, shape manipulation, shape parametrization, statistical models, and research trends. Application areas include, but are not limited to: computer-aided design (CAD), architecture and urban modeling, computer vision (like the Microsoft Kinect), 3D printing and scanning, medical imaging and analysis, and yes, creating characters and props for movies and games.
Day | Topic | Slides | Handouts and Reading |
---|---|---|---|
Jan 9 | Introduction | 01_intro | |
Jan 12 | Point Clouds - I | 02_points | |
Jan 16 | Point Clouds - II | 03_points |
J. P. Lewis, 3 Derivations of PCA Jon Shlens, PCA Tutorial Dave Eberly, Least Squares Fitting (see Sec 4) mlai@stackoverflow: A Visual Explanation of the Hough Transform Dana Ballard, Generalizing the Hough Transform |
Jan 19 | Point Clouds - III | (contd) | |
Jan 23 | Polygon Meshes | 04_meshes | |
Jan 30 | Meshes: Memory Formats | 05_meshes | |
Feb 2 | Mesh Reconstruction from Points | 06_reconst |
Steven Fortune, Voronoi Diagrams and Delaunay Triangulations Emo Welzl, Delaunay Triangulations |
Feb 6 | Poisson Surface Reconstruction - I | 07_reconst |
Jo Ellis-Monaghan, Vector Operators David Bindel, Linear Least Squares Misha Kazhdan, The Poisson Equation Kazhdan et al., Poisson Surface Reconstruction |
Feb 9 | Poisson Surface Reconstruction - II | 08_reconst | |
Feb 13 | Polygonization of Implicit Surfaces | 09_polygonize |
Lorensen and Cline, Marching Cubes StackOverflow, Marching cubes vs marching tetrahedra |
Feb 16 | Mesh Simplification | 10_simplify |
Michael Floater, Mesh Simplification and Optimization Rossignac/Borrel, Multi-Resolution 3D Approximations for Rendering Complex Scenes Greg Turk, Re-tiling Polygonal Surfaces Hoppe et al., Mesh Optimization Garland/Heckbert, Surface Simplification Using Quadric Error Metrics |
Feb 27 | Mesh Simplification (contd) | ||
Mar 2 | Distances on Surfaces | 11_distances | |
Mar 6 | Exact and Approximate Shortest Paths |
12_shortest |
Surazhsky et al., Fast Exact and Approximate Geodesics on Meshes Yan-Bin Jia, Geodesics |
Mar 9 | Differential Geometry of Curves and Surfaces |
13_surfcurv (+ handouts) |
Mirela Ben-Chen, Differential Geometry of Curves (Note Slide 4: "differentiable", as used here to imply having derivatives of all orders, is elsewhere termed "smooth" or "analytic") Lia Vas, Curves Jean Gallier, "Differential Geometry of Surfaces" part 1, part 2, part 3 Lia Vas, "Surfaces" part 1, part 2, part 3 |
Mar 16 | Differential Geometry of Curves and Surfaces (contd) |
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Mar 20 | Shape Descriptors - I | 14_features | |
Mar 23 | Shape Descriptors - II | (handouts) | Tom Funkhouser, "Shape Descriptors" part 1, part 2 |
Mar 27 | Shape Descriptors - III | 16_features |
Chen et al., On Visual Similarity Based 3D Model Retrieval Su et al., Multi-view Convolutional Neural Networks for 3D Shape Recognition Christopher Olah, ConvNets: A Modular Perspective Andrej Karpathy, Convolutional Neural Networks (part of larger course on same topic) |
Mar 30 | (discussion) | ||
Apr 3 | Shape Segmentation | (handouts) |
Qixing Huang, Shape Segmentation Kalogerakis et al., Learning Mesh Segmentation and Labeling Huang/Koltun, Joint Shape Segmentation with Linear Programming Stephen Gould, Markov Random Fields for Computer Vision |
Apr 6 | Laplacian Mesh Processing | 18_laplace |
Olga Sorkine, Laplacian Mesh Processing Lévy and Zhang, Spectral Mesh Processing Sun et al., "Heat Kernel Signature": slides, paper |
Apr 10 | Shape Parametrization | (handouts) | Alla Sheffer, "Parametrization" part 1, part 2, part 3 |
All deadlines are at 11:59pm.