Search results for "Quaternion"

On Barbilian spaces in projective lattice geometries

1992

We introduce the notion of a Barbilian space of a projective lattice geometry in order to investigate the relationship between lattice-geometric properties and the properties of point-hyperplane structures associated with. We obtain a characterization of those projective lattice geometries, the Barbilian space of which is a Veldkamp space.

On the representation of integers by indefinite binary Hermitian forms

2011

Given an integral indefinite binary Hermitian form f over an imaginary quadratic number field, we give a precise asymptotic equivalent to the number of nonequivalent representations, satisfying some congruence properties, of the rational integers with absolute value at most s by f, as s tends to infinity.

Experimental validation of a quaternion-based attitude estimation with direct input to a quadcopter control system

2013

This paper presents a method to calculate the attitude quaternion of a quadcopter with few calculations. The quaternion calculation is based on accelerometers and gyroscopes from an Inertial Measurement Unit (IMU). The quaternion from the accelerometer is calculated as the shortest rotation arc from the gravity vector in the navigation frame. The quaternion from the gyroscope is calculated based on equations of the quaternion derivative. A complementary filter is combining the two quaternions with a componentwise comparison. The attitude estimation is calculated without any trigonometric functions. The quaternion is directly used as an input to the attitude controller. The attitude controll…

Linear Wave Equations and Effective Lagrangians for Wigner Supermultiplets

1995

The relevance of the contracted SU(4) group as a symmetry group of the pion nucleon scattering amplitudes in the large $N_c$ limit of QCD raises the problem on the construction of effective Lagrangians for SU(4) supermultiplets. In the present study we suggest effective Lagrangians for selfconjugate representations of SU(4) in exploiting isomorphism between so(6) and ist universal covering su(4). The model can be viewed as an extension of the linear $\sigma$ model with SO(6) symmetry in place of SO(4) and generalizes the concept of the linear wave equations for particles with arbitrary spin. We show that the vector representation of SU(4) reduces on the SO(4) level to a complexified quatern…

3D modul for syntetisk kalkulator

2006

Masteroppgave i informasjons- og kommunikasjonsteknologi 2006 - Høgskolen i Agder, Grimstad ActionScript er et språk som har blitt benyttet mer og mer de senere årene og er en del av verktøyet Flash. Dette er et design verktøy som har gode metoder for animasjoner i 2D og genererer små filer som gjør det svært egnet for internett. Denne rapporten ser på mulighetene for å generere, håndtere og visualisere tredimensjonale objekter i Flash ved bruk av ActionScript. Det blir diskutert roteringsmatriser opp mot Quaternion rotasjon og isometrisk projeksjon opp mot perspektivisk projeksjon i forhold til 3D objekter. Rapporten tar for seg ulike kurver og flater og hvilke begrensninger ActionScript h…

Fast Volumetric Reconstruction of Human Body through Superquadrics

2013

This paper describes a technique to reconstruct the volumes of the human body. For this purpose, are introduced mathematical objects able to represent 3d shapes, called super quadrics. These objects are positioned in the space according the captures made by a Microsoft Kinect device and are composed to represent the volumes of the human body. The employment of quaternions provides a relevant speedup for the rotation of the volumes and allows to follow the human movements in real time and reduced computational cost.

Locally compact (2, 2)-transformation groups

2010

We determine all locally compact imprimitive transformation groups acting sharply 2-transitively on a non-totally disconnected quotient space of blocks inducing on any block a sharply 2-transitive group and satisfying the following condition: if Δ1, Δ2 are two distinct blocks and Pi, Qi ∈ Δi (i = 1, 2), then there is just one element in the inertia subgroup which maps Pi onto Qi. These groups are natural generalizations of the group of affine mappings of the line over the algebra of dual numbers over the field of real or complex numbers or over the skew-field of quaternions. For imprimitive locally compact groups, our results correspond to the classical results of Kalscheuer for primitive l…

Irreducible components of Hurwitz spaces of coverings with two special fibers

2013

In this paper we prove new results of irreducibility for Hurwitz spaces of coverings whose monodromy group is a Weyl group of type B_d and whose local monodromies are all reflections except two.

A classification of $\protect \mathbb{R}$-Fuchsian subgroups of Picard modular groups

2018

Characterization of strong chain geometries by their automorphism group

1992

A wide class of chain geometries is characterized by their automorphism group using properties of a distinguished involution.