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.

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

Vertices of the 4-dimensional semi-regular polytope, the grand antiprism and its symmetry group of order 400 are represented in terms of quaternions with unit norm. It follows from the icosian representation of the E8 root system which decomposes into two copies of the root system of H4. The symmetry of the grand antiprism is a maximal subgroup of the Coxeter groupW (H4). It is the groupAut(H2⊕...