In 1853 Hamilton showed that a general linear vector transformation in three dimensions satisfied a third-order equation. In this paper we indicate how Hamilton came to consider this transformation and what he did with it. Hamilton’s work was written in the language of quaternions, which he invented. We describe this work using vectors instead of the quaternions. In addition, we express Hamilto...

Dual quaternions and dual quaternion interpolation are powerful mathematical tools for the spatial analysis of rigid body motions. In this paper, after a review of some basic results and formulas, it will be presented an attempt to use these tools for the the kinematic modeling of human joints. In particular, the kinematic parameters extracted from experimentally acquired data are compared with...

In this contribution we generalize the classical Fourier Mellin transform [3], which transforms functions f representing, e.g., a gray level image defined over a compact set of R. The quaternionic Fourier Mellin transform (QFMT) applies to functions f : R → H, for which |f | is summable over R+ × S under the measure dθ dr r . R ∗ + is the multiplicative group of positive and non-zero real numbe...

We consider the problem of interpolating a smooth curve to a point sequence in the unit quaternion space U. This problem has application to object orientation interpolation in computer animation , sweep surface generation in solid modeling[7, 6]. Since the unit quaternions form the unit sphere 8 3 in p;4, a simple curve scheme using spherical biarcs is presented to solve this problem. The spher...

Computer vision and robotics suffer from not having good tools for manipulating three-dimensional objects. Vectors, coordinate geometry, and trigonometry all have deficiencies. Quaternions can be used to solve many of these problems. Many properties of quaternions that are relevant to computer vision and robotics are developed. Examples are given showing how quaternions can be used to simplify ...