“Geometric Algebra” by Naeve, Rockwood, Doran, Lasenby, Dorst, et al. …

  • ©Ambjorn Naeve, Alyn P. Rockwood, Chris Doran, Joan Lasenby, Leo Dorst, David Hestenes, and Stephen Mann


Abstract:


    Prerequisites
    An interest in the mathematical fundamentals of computer graphics. Familiarity with vector calculus, complex analysis, homogeneous coordinates, and linear algebra. A reasonable level of mathematical maturity ensures optimum absorption of the breadth of topics presented.

    Topics
    An introduction to geometric algebra. An improved model for generalized homogeneous space, fast intersection methods of planes and spheres, new ways to view con-formal maps, interactive projective geometry, methods for articulated systems and robotics, shape extraction and motion capture from scenes, elastic reformations and educational implications.

    Description
    Geometric algebra unifies many different and redundant mathematical systems in current use, and it has wide application in computer graphics: kinematics and dynamics, simplicial calculations (polygons, FEM), fluid flow, collision detection, quaternion splines, elastic deformations, curve and surface definition, vector fields, etc. In this course, attendees explore a new, fundamental language for the mathematics of computer graphics, as well as for modeling and interactive techniques in general.

     


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