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The purpose of this course is to cover the fundamentals of geometric modeling in computer graphics. 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 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

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 January 2, 2005.