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Geometric Algebra: New Foundations, New Insights CAL
level 12
Geometric algebra is a new fundamental language for the mathematics of computer graphics, modeling, and interactive techniques. It is especially useful for handling geometric problems, since it allows for intrinsic (coordinate-free) and dimensionally seamless descriptions of geometry. It has generated new insights and improved algorithms in a wide array of computer graphics applications: kinematics and dynamics, simplicial calculations (polygons, FEM), fluid flow, collision detection, hierarchical bounding spheres, boxes, quaternion splines on spheres, elastic deformations, curve and surface definition, vector fields, etc.

An active interest in mathematical fundamentals for computer graphics, and related areas. A reasonable level of mathematical maturity ensures maximal absorption of the breadth of topics, but the presentation is also geared for those who want to glean the highlights, even without a full understanding of all the details.

An introduction to geometric algebra, an improved model for generalized homogeneous space, fast intersection methods of planes and spheres, new ways to view conformal maps, projective geometry, methods for articulated systems and robotics, shape extraction and motion capture from scenes, elastic deformations, and educational implications and approaches.

Alyn Rockwood
Mitsubishi Electric Research Laboratory

Chris Doran
Joan Lasenby

Cambridge University

Leo Dorst
University of Amsterdam

David Hestenes
Arizona State University

Stephen Mann
University of Waterloo

Ambjorn Naeve
Swedish Royal Institute of Technology

Alyn Rockwood
Mitsubishi Electric Research Laboratory


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