In this paper we introduce the continuous quaternion wavelet transform (CQWT). We express the admissibility condition in terms of the (right-sided) quaternion Fourier transform. We show that its fundamental properties, such as inner product, norm relation, and inversion formula, can be established whenever the quaternion wavelets satisfy a particular admissibility condition. We present several ...

To provide efficient tools for the capture and modeling of acceptable virtual human poses, we propose a method for constraining the underlying joint structures based on real life data. Current tools for delimiting valid postures often employ techniques that do not represent joint limits in an intuitively satisfying manner, and furthermore are seldom directly derived from experimental data. Here...

Though Combination of Quaternions and matrix has been a popular tool in skeletal animation for more than 20 years, classical quaternions are restricted to the representation of rotations. In skeletal animation and many other applications of 3D computer graphics, we actually deal with rigid transformation including both rotation and translation. Dual quaternions represent rigid transformations n...

We introduce three universality classes of chiral random matrix ensembles with a nonzero chemical potential and real, complex or quaternion real matrix elements. In the thermodynamic limit we find that the distribution of the eigenvalues in the complex plane does not depend on the Dyson index, and is given by the solution proposed by Stephanov. For a finite number of degrees of freedom, N , we ...

Accurate and real-time tracking of the orientation or attitude of rigid bodies has traditional applications in robotics, aerospace, underwater vehicles, human body motion capture, etc. Towards human body motion capture, especially wearable devices, the use of a longer time has always been a challenge for several weeks or several months continuously, so a low-cost chip and a low computational co...

A 4D rotation can be decomposed into a left-isoclinic and a right-isoclinic rotation. This decomposition, known as Cayley’s factorization of 4R rotations, can be performed using Elfrinkhof-Rosen method. In this paper, we present a more straightforward alternative approach based on the fact that there is an orthogonal basis, in the sense of Hilbert-Schmidt, for the space of 4×4 real orthonormal ...