Foundations of Geometric Algebra computing
Abstract
Geometric Algebra has the power to lead easily from the geometric intuition of solving an engineering application to its efficient implementation on current and future computing platforms. It is easy to develop new algorithms in areas such as computer graphics, robotics, computer animation and computer simulation. Owing to its geometric intuitiveness, compactness and simplicity, algorithms based on Geometric Algebra can lead to enhanced quality, a reduction in development time and solutions that are more easily understandable and maintainable. Often, a clear structure and greater elegance result in lower runtime performance. However, based on our computing technology, Geometric Algebra implementations can even be faster and more robust than conventional ones. We present an example on how easy it is to describe algorithms in Geometric Algebra and introduce our technology for the integration of Geometric Algebra into standard programming languages. We really do hope that this technology can support the widespread use of Geometric Algebra Computing technology in many engineering fields.
 Publication:

Numerical Analysis and Applied Mathematics ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics
 Pub Date:
 September 2012
 DOI:
 10.1063/1.4756054
 Bibcode:
 2012AIPC.1479...27H
 Keywords:

 algebra;
 computational geometry;
 programming languages;
 02.10.v;
 45.10.Na;
 89.20.Kk;
 Logic set theory and algebra;
 Geometrical and tensorial methods;
 Engineering