In this paper, the problem of automatic dance performance evaluation from human Motion Capture (MoCap) data, is addressed. A novel framework is presented, using data captured by Kinect-based human skeleton tracking, where the evaluation of user’s performance is achieved against a goldstandard performance of a teacher. The framework addresses several technical challenges, including global and lo...

The main topics of this technical report are quaternions, their mathematical properties, and how they can be used to rotate objects. We introduce quaternion mathematics and discuss why quaternions are a better choice for implementing rotation than the well-known matrix implementations. We then treat di erent methods for interpolation between series of rotations. During this treatment we give co...

An involution or anti-involution is a self-inverse linear mapping. In this paper, we will present two real quaternion matrices, one corresponding to a real quaternion involution and one corresponding to a real quaternion anti-involution. Moreover, properties and geometrical meanings of these matrices will be given as reflections in R^3.

Let V be a finite dimensional complex vector space and W ⊂ GL(V ) be a finite complex reflection group. Let V reg be the complement in V of the reflecting hyperplanes. A classical conjecture predicts that V reg is a K(π, 1) space. When W is a complexified real reflection group, the conjecture follows from a theorem of Deligne, [20]. Our main result validates the conjecture for duality (or, equi...

in this paper, two new hamilton operators are defined and the algebra of dual split quaternions isdeveloped using these operators. it is shown that finite screw motions in minkowski 3-space can be expressedby dual-number ( 3×3 ) matrices in dual lorentzian space. moreover, by means of hamilton operators, screwmotion is obtained in 3-dimensional minkowski space 3r1

Motivated by topological quantum field theory, we investigate the geometric aspects of unitary 2-representations of finite groups on 2-Hilbert spaces, and their 2-characters. We show how the basic ideas of geometric quantization are ‘categorified’ in this context: just as representations of groups correspond to equivariant line bundles, 2-representations of groups correspond to equivariant gerb...

We give an overview of recent advances in analysis of equations of electrodynamics with the aid of biquaternionic technique. We discuss both models with constant and variable coefficients, integral representations of solutions, a numerical method based on biquaternionic fundamental solutions for solving standard electromagnetic scattering problems, relations between different operators of mathe...