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This course is an upper level undergraduate / graduatelevel introduction to the mathematical methods used in modeling and processing geometric shapes for use in CAD/CAM, computer graphics (gaming / special effects), 3D computer vision, and in many other areas of science, engineering, and commerce. Topics to be covered include material on both designed shapes (classical CAGD) and on shapes acquired through sensors (geometry processing). While the focus of the course is on classical methods, machine learning tools for shape analysis and content creation will also be introduced.
 Homogeneous Coordinates and Geometric Transformations
 Quaternions and their Use in Modeling 3D Rotations and Rigid Motions
 Parametric and Implicit Representations for Curves
 Algebraic Classification of the Parametric Polynomial Curves of Low
Degree
 Polar Forms and the de Calsteljau Subdivision Algorithm
 The Bézier Representation and the Bernstein Basis
 Splines and Continuity Constraints
 BSplines and the de Boor Algorithm
 Rational Curves
 Parametric Polynomial Surfaces and NURBS
 Subdivision Curves and Surfaces
 Triangle Meshes for Surface Representation and Reconstruction
 The QuadEdge Data Structure for Manifold Subdivision
 Scan Alignment and Shape Matching
 Surface Reconstruction from Scattered Points
 Machine Learning Approaches to Shape Analysis
 Mesh Simplification, Smoothing and Fairing
 Mesh Remeshing and Parametrization
 Generative Models Based on Learned Shape Representations and Applications
The course requires background in linear algebra and elementary discrete algorithms.
Students taking the course for credit will
be expected to:
 be present and actively participate in class
 do a number of paperandpencil homeworks
 take the class midterm
 do a programming assignment or project
These pages are maintained by Leonidas Guibas guibas@cs.stanford.edu.
Last update March 9, 2021.
