Course Information

About the course

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.