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 ...

In this work, we communicate the topic of complex Lie algebroids based on the extended fractional calculus of variations in the complex plane. The complexified Euler–Lagrange geodesics and Wong’s fractional equations are derived. Many interesting consequences are explored.

Complexified spacetime algebra is defined as the geometric (Clifford) algebra of spacetime with complex coefficients. By resorting to matrix representation by means of Dirac-Pauli gamma matrices, the paper demonstrates isomorphism between subalgebras of CSTA and SU(3). It is shown that the symmetry group of those subalgebras is indeed U(1) ⊗ SU(2) ⊗ SU(3) and that there are 4 distinct copies of...