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Given a parameterized space of square matrices, the associated set of eigenvectors forms some kind of a structure over the parameter space. When is that structure a vector bundle? When is there a vector field of eigenvectors? We answer those questions in terms of three obstructions, using a Homotopy Theory approach. We illustrate our obstructions with five examples. One of those examples gives ...

We examine corresponding Cauchy-Riemann equations by using the non-commutativity for the product on split-biquaternions. Additionally, we describe the regularity of functions and properties of their differential equations on split-biquaternions. We investigate representations and calculations of the derivatives of functions of split-biquaternionic variables. c ©2016 all rights reserved.

The biquaternion (complexified quaternion) algebra contains idempotents (elements whose square remains unchanged) and nilpotents (elements whose square vanishes). It also contains divisors of zero (elements with vanishing norm). The idempotents and nilpotents are subsets of the divisors of zero. These facts have been reported in the literature, but remain obscure through not being gathered toge...

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...

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...

In this paper we generalize established techniques and blending algorithm for quaternions to dual quaternions to represent rigid transformations compactly. With the visualization of OpenGL, we employ dual quaternions to achieve character animation in real time. Classical quaternions are only able to characterize rotations although combination of matrix calculation and quaternions operator has b...