This course is a graduatelevel introduction to the mathematical
methods used in modeling geometric shapes for use in CAD/CAM, computer
graphics (gaming / special effects), and so on. Topics to be covered include:
 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
 Constructive Solid Geometry, Binary Space Partitions, and Conversion
Algorithms
 Surface Reconstruction from Scattered Data Points
 Mesh Simplification and Compression, as well as other Geometry Processing Algorithms
The course requires some background in linear algebra and elementary
discrete algorithms.
The class will consist of lectures by the instructor and a recitation
section organized by the TA. Students taking the course for credit will
be expected to:
 be present and actively participate in class
 do a number of paper and pencil homeworks
 take the class midterm
 do a programming project
These pages are maintained by Leonidas Guibas guibas@cs.stanford.edu.
Last update September 24, 2006.
