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 4 | Introduction | 01_intro | |
Jan 7 | Point Clouds | 02_points | |
Jan 11 | More Point Clouds | 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 14 | Polygon Meshes | 04_meshes | |
Jan 18 | Meshes: Memory Formats | 05_meshes | |
Jan 21 | Mesh Reconstruction from Points | 06_reconst |
Steven Fortune, Voronoi Diagrams and Delaunay Triangulations Emo Welzl, Delaunay Triangulations Kazhdan et al., Poisson Surface Reconstruction Jo Ellis-Monaghan, Vector Operators David Bindel, Linear Least Squares |
Jan 25 | Poisson Surface Reconstruction 2/3 | 07_reconst |
Misha Kazhdan, The Poisson Equation |
Jan 28 | Poisson Surface Reconstruction 3/3 | 08_reconst | |
Feb 1 | Polygonization of Implicit Surfaces | 09_polygonize | Lorensen and Cline, Marching Cubes |
Feb 4 | 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 8 | Distances on Surfaces | 11_distances | |
Feb 11 | Exact and Approximate Shortest Paths |
12_shortest |
Surazhsky et al., Fast Exact and Approximate Geodesics on Meshes Yan-Bin Jia, Geodesics |
Feb 15 | Curves | (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 |
Feb 18 | Surface Curvature | 14_surfcurv |
Jean Gallier, "Differential Geometry of Surfaces" part 1, part 2, part 3 Lia Vas, "Surfaces" part 1, part 2, part 3 |
Feb 29 | Shape Descriptors - I | 15_features | |
Mar 3 | Shape Descriptors - II | (handouts) | Tom Funkhouser, "Shape Descriptors" part 1, part 2 |
Mar 7 | Shape Descriptors - III | 17_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 14 | Laplacian Mesh Processing | 18_laplace | Olga Sorkine, Laplacian Mesh Processing |
Mar 17 | Spectral Mesh Analysis | (handouts) |
Lévy and Zhang, Spectral Mesh Processing Sun et al., "Heat Kernel Signature": slides, paper |
Mar 21 | Spectral Mesh Analysis | 20_spectral | |
Mar 24 | Shape Segmentation | (handouts) |
Qixing Huang, Shape Segmentation Kalogerakis et al., Learning Mesh Segmentation and Labeling Huang/Koltun, Joint Shape Segmentation with Linear Programming |
Mar 28 | Shape Segmentation | ||
Mar 31 | Shape Segmentation | Stephen Gould, Markov Random Fields for Computer Vision | |
Apr 4 | Shape Parametrization | (handouts) | Alla Sheffer, "Parametrization" part 1, part 2, part 3 |
Apr 7 | Shape Parametrization | ||
Apr 11 | Data-Driven Design | 26_dddesign |
All deadlines are at 11:59pm.