“Geometric Algebra: New Foundations, New Insights” by Naeve, Rockwood, Doran, Lasenby, Dorst, et al. …

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

Conference:


Entry Number: 31

Title:

    Geometric Algebra: New Foundations, New Insights

Course Organizer(s):



Presenter(s):



Abstract:


    Prerequisites
    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. 

    Topics
    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.

    Description
    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. 

     


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