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...

Figure 1: A comparison of dual quaternion skinning with previous methods: log-matrix blending Cordier and Magnenat-Thalmann 2005 and. Dual quaternions a generalization of regular quaternions invented. Techdocslcoterrors.pdf.Figure 1: A comparison of dual quaternion skinning with previous methods: log-matrix. Closed-form approximation, based on dual quaternions a general.Skinning with Quaternion...

This paper presents a computationally-fast inverse dynamics model based on unit quaternion orientation representation for use in the generation of unmanned aircraft trajectories when the flight envelope may include all flight path orientations, a necessary attribute for aerobatics or unmanned air-to-air combat vehicles. The model removes the inherent singularities in Euler-angle attitude repres...

Second order statistics of quaternion random variables and signals are revisited in order to exploit the complete second order statistical information available. The conditions for Q-proper (second order circular) random processes are presented, and to cater for the non-vanishing pseudocovariance of such processes, the use of ı-E-k-covariances is investigated. Next, the augmented statistics and...

By a theorem of Elman and Lam, fields over which quadratic forms are classified by the classical invariants dimension, signed discriminant, Clifford invariant and signatures are exactly those fields F for which the third power IF of the fundamental ideal IF in the Witt ring WF is torsion free. We study the possible values of the uinvariant (resp. the Hasse number ũ) of such fields, i.e. the sup...

We introduce a symplectic dual quaternion variational integrator(DQVI) for simulating single rigid body motion in all six degrees of freedom. Dual quaternion is used to represent rigid body kinematics and one-step Lie group variational integrator is used to conserve the geometric structure, energy and momentum of the system during the simulation. The combination of these two becomes the first L...

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.