Applications of Clifford Algebra in Mixed Reality Environment

Abstract

The 'beauty' of Clifford's Geometric Algebras is its ability to incorporate other algebras and it is the 'mother' algebra for all algebras. This paper introduces the advantage of using this algebra by combining and augmenting certain group of algebras, such as linear algebra, quaternion algebra, the Grassmann algebra and projective algebra to simplify mathematical manipulations in 3-dimensional rotations and projective geometry, especially in the context of mixed reality environment. Those 'augmented' representations are shown with applications in the mixed reality environment, especially for registration and computer vision based object recognition issues. Some simple scenarios with place-holder objects are described at the end for a full understanding of the mixed reality applications before other most recent engineering and computer science areas using this algebra for their applications are briefly discussed.