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This course is a graduate-level 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 3-d 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
  • B-Splines and the de Boor Algorithm
  • Rational Curves
  • Parametric Polynomial Surfaces and NURBS
  • Subdivision Curves and Surfaces
  • Triangle Meshes for Surface Representation and Reconstruction
  • The Quad-Edge 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
Last update September 24, 2006.