3 Quaternion Representation 5 3.1 Axis-Angle to Quaternion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3.2 Quaternion to Axis-Angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3.3 Quaternion to Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.4 Matrix to Quaternion . . . . . . . . . . ....

Three-axis-magnetometers (TAMs) are widely utilized as a key component of attitude determination subsystems and as such are considered the corner stone of navigation for low Earth orbiting (LEO) space systems. Precise geomagnetic-based navigation demands accurate calibration of the magnetometers. In this regard, a complete online calibration process of TAM is developed in the current research t...

An algorithm is presented that constructs a C 2-continuous B-spline quaternion curve which interpolates a given sequence of unit quaternions on the rotation group SO(3). The de Casteljau type construction method of B-spline curves can be extended to generate B-spline quaternion curves Sch92]; however, the B-spline quaternion curves do not have C 2-continuity in SO(3). The authors KKS94a] recent...

The smooth interpolation of keyframes of a rigid body, in particular their orientations, is an important problem in animation . Using the quaternion as a representation for orientation, several papers have solved this problem through the generation of smooth curves on the quaternion sphere. However, none of these methods have constructed rational curves. This paper develops a method for generat...

A method of reducing general quaternion functions of first degree, i.e., linear quaternion functions, to quaternary canonical form is given. Linear quaternion functions, once reduced to canonical form, can be maintained in this form under functional composition. Furthermore, the composition operation is symbolically identical to quaternion multiplication, making manipulation and reduction of sy...

An involution or anti-involution is a self-inverse linear mapping. In this paper, we will present two real quaternion matrices, one corresponding to a real quaternion involution and one corresponding to a real quaternion anti-involution. Moreover, properties and geometrical meanings of these matrices will be given as reflections in R^3.

In this paper, a quaternion firefly algorithm is utilized to solve a multi-row facility layout design problem with the objective of minimizing the total cost of transportation. A quaternion firefly algorithm takes the motion of the firefly as a quaternion one. Consequently, the solution space is explored more accurately and the answers are of higher quality. That is, the answers are considerabl...

abstract background and purpose:vector-borne diseases such as malaria and leishmaniasis are still a public health problem in iran. one of the effective ways to prevent of these diseases is to improve the vector control program. we carried out this study for assessment managers of school knowledge, attitude and practice regarding vector control programs. materials and methods:a cross-sectional s...