This paper introduces the mathematical framework of conformal geometric algebra (CGA) as a language for computer graphics and computer vision. Specifically it discusses a new method for pose and position interpolation based on CGA which firstly allows for existing interpolation … Continued
Projective geometry provides the preferred framework for most implementations of Euclidean space in graphics applications. Translations and rotations are both linear transformations in projective geometry, which helps when it comes to programming complicated geometrical operations. But there is a fundamental … Continued
Recent developments in geometric algebra have shown that by moving from a projective to a conformal representation (5d representation of 3d space), one is able to extend the range of geometrical operations that can be carried out in an efficient … Continued
J. Lasenby and A. Stevenson, Using geometric algebra in optical motion capture, In: E. Bayro and G. Sobczyk eds. Geometric algebra: a geometric approach to computer vision, neural and quantum computing, robotics and engineering. Birkhauser 2000. PDF
While the early applications of geometric algebra (GA) were confined to physics, there has been significant progress over recent years in applying geometric algebra to areas of engineering and computer science. The beauty of using the same language for these … Continued
The late 18th and 19th centuries were times of great mathematical progress. Many new mathematical systems and languages were introduced by some of the millenium’s greatest mathematicians. Amongst these were the algebras of Clifford (1878) and Grassmann (1877). While these … Continued
We discuss a coordinate-free approach to the geometry of computer vision problems. The technique we use to analyse the 3-dimensional transformations involved will be that of geometric algebra: a framework based on the algebras of Clifford and Grassmann. This is … Continued