A brief introduction to Clifford algebra

Geometric algebra (also known as Clifford algebra) is a powerful mathematical tool that offers a natural and direct way to model geometric objects and their transformations. It is gaining growing attention in different research fields as physics, robotics, CAD/CAM and computer graphics. Clifford algebra makes geometric objects (points, lines and planes) into basic elements of computation and defines few universal operators that are applicable to all types of geometric elements. This paper provides an introduction to Clifford algebra elements and operators.

[1]  Jaap Suter,et al.  Geometric Algebra Primer , 2003 .

[2]  Giorgio Vassallo,et al.  CliffoSor: a parallel embedded architecture for geometric algebra and computer graphics , 2005, Seventh International Workshop on Computer Architecture for Machine Perception (CAMP'05).

[3]  Giorgio Vassallo,et al.  An embedded, FPGA-based computer graphics coprocessor with native geometric algebra support , 2009, Integr..

[4]  Leo Dorst,et al.  Modeling 3D Euclidean Geometry , 2003, IEEE Computer Graphics and Applications.

[5]  Leo Dorst,et al.  Honing geometric algebra for its use in the computer sciences , 2001 .

[6]  David Hestenes.  New Foundations for Classical Mechanics , 1986 .

[7]  Giorgio Vassallo,et al.  An FPGA Implementation of a Quadruple-Based Multiplier for 4D Clifford Algebra , 2008, 2008 11th EUROMICRO Conference on Digital System Design Architectures, Methods and Tools.

[8]  Leo Dorst,et al.  Geometric Algebra , 2019, Computer Vision, A Reference Guide.

[9]  Giorgio Vassallo,et al.  A Sliced Coprocessor for Native Clifford Algebra Operations , 2007 .

[10]  Gerald Sommer,et al.  Implementation of a Clifford Algebra Co-Processor Design on a Field Programmable Gate Array , 2004 .

[11]  Leo Dorst,et al.  Geometric algebra: A computational framework for geometrical applications (Part I: Algebra) , 2002 .

[12]  D. Hestenes,et al.  Clifford Algebra to Geometric Calculus: A Unified Language for Mathematics and Physics , 1984 .

[13]  Giorgio Vassallo,et al.  CliffoSor, an Innovative FPGA-based Architecture for Geometric Algebra , 2005, ERSA.

[14]  Stephen Mann,et al.  Geometric Algebra: A Computational Framework for Geometrical Applications (Part 2) , 2002, IEEE Computer Graphics and Applications.

[15]  D. Dijkman.  Efficient Implementation of Geometric Algebra , 2007 .

[16]  David Zeltzer.  Interacting with virtual worlds , 1991 .