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 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
(+ 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)
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.