This paper presents a method to smoothly interpolate a given sequence of solid orientations using circular blending quaternion curves. Given three solid orientations, a circular quaternion curve is constructed that interpolates the three orientations. Therefore, given four orientations q i?1 ; q i ; q i+1 ; q i+2 , there are two circular quaternion curves C i and C i+1 which interpolate the tri...

Unit quaternion is an ideal parameterization for joint rotations. However, due to the complexity of the geometry of S group, it’s hard to specify meaningful joint constraints with unit quaternion. In this paper, we have proposed an effective and accurate method to specify the rotation limits for joints parameterized with the unit quaternion. Joint constrains constructed with our method are adeq...

The natural mapping of the right quaternion vector space H onto the quaternion projective line (identified with the four-sphere) can be defined for complex quaternions H ⊗R C as well. We discuss its exceptional set, the fiber subspaces, and how the linear automorphism groups of two-dimensional quaternion vector spaces and modules induce groups of projective automorphisms of the image quadrics.

We define zonal polynomials of quaternion matrix argument and deduce some important formulae of zonal polynomials and hypergeometric functions of quaternion matrix argument. As an application, we give the distributions of the largest and smallest eigenvalues of a quaternion central Wishart matrix W ∼ QW (n,Σ), respectively.

We study the quaternion CR-submanifolds of a quaternion Kaehler manifold. More specifically we study the properties of the canonical structures and the geometry of the canonical foliations by using the Bott connection and the index of a quaternion CR-submanifold. 2000 Mathematics Subject Classification. 53C20, 53C21, 53C25.

Lattices are a popular field of study in mathematical research, but also more practical areas like cryptology or multiple-input/multiple-output (MIMO) transmission. In theory, most often lattices over real numbers considered. However, communications, complex-valued processing is usually interest. Besides, by the use dual-polarized transmission as well combination two time slots frequencies, fou...

Facial expression recognition is an important technology in human-computer interaction. This study investigates a method for facial expression recognition using quaternion neural networks. A multi-layer quaternion neural network that conducts its learning using a quaternion back-propagation algorithm is employed to design the facial expression recognition system. The input feature vector of the...

Quaternion derivatives exist only for a very restricted class of analytic (regular) functions; however, in many applications, functions of interest are real-valued and hence not analytic, a typical case being the standard real mean square error objective function. The recent HR calculus is a step forward and provides a way to calculate derivatives and gradients of both analytic and non-analytic...