Results 31 to 40 of about 634 (251)
CoRR, 2023 Transformations in the field of computer graphics and geometry are one of the most important concepts for efficient manipulation and control of objects in 2-dimensional and 3-dimensional space. Transformations take many forms each with their advantages and disadvantages.
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Dual-Quaternion Analytic LQR Control Design for Spacecraft Proximity Operations
Sensors, 2021 Proximity operations offer aggregate capability for a spacecraft operating in close proximity to another spacecraft, to perform on-orbit satellite servicing, or to a space object to perform debris removal. To utilize a spacecraft performing such advanced
Kyl Stanfield, Ahmad Bani Younes
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THE CORRESPONDING CAUCHY - RIEMANN SYSTEM FOR DUAL QUATERNION-VALUED FUNCTIONS
Проблемы анализа, 2018 This paper provides differential operators in dual quaternions and represents the regularity of dual quaternionvalued functions using the dual Cauchy - Riemann system in dual quaternions.
Kim J.E.
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A Closed-Form Solution to Planar Feature-Based Registration of LiDAR Point Clouds
ISPRS International Journal of Geo-Information, 2021 Since pairwise registration is a necessary step for the seamless fusion of point clouds from neighboring stations, a closed-form solution to planar feature-based registration of LiDAR (Light Detection and Ranging) point clouds is proposed in this paper ...
Yongbo Wang, Nanshan Zheng, Zhengfu Bian
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Communications, Faculty Of Science, University of Ankara Series A1Mathematics and Statistics, 2010 Summary: Serret-Frenet and parallel-transport frame are produced with the help of reel quaternions again by \textit{A. J. Hanson} [Quaternion Frenet frames: making optimal tubes and ribbons from curves (1994)]. In this study, calculations mentioned above are applied to dual quaternions and the Serret-Frenet and parallel-transport frame are obtained by ...
ÖZTÜRK, Ufuk +3 more
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The Regularity of Functions on Dual Split Quaternions in Clifford Analysis
Abstract and Applied Analysis, 2014 This paper shows some properties of dual split quaternion numbers and expressions of power series in dual split quaternions and provides differential operators in dual split quaternions and a dual split regular function on Ω⊂ℂ2×ℂ2 that has a dual split ...
Ji Eun Kim, Kwang Ho Shon
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Dual transformations and quaternions
Mathematical Methods in the Applied Sciences, 2021 In this study, we are interested in the way quaternions to represent 3D and 4D rotations in Lorentzian space. We give a new method for obtaining a rotation matrix in Lorentzian space with the help of a unit quaternion. Furthermore, we prove that rotation matrices correspond to a quaternion leave invariant the same axis in Euclidean and Lorentzian space.
Gülsüm Yüca, Yusuf Yaylı
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Modified Hand–Eye Calibration Using Dual Quaternions
Applied Sciences, 2022 This paper presents a modified model for hand–eye calibration based on dual quaternion algebra. By using dual quaternions to represent the rotations and translations of a rigid body simultaneously in the task space, the formulation is elegant for the ...
Guozhi Li +3 more
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DUAL QUATERNIONIC REGULAR FUNCTION OF DUAL QUATERNION VARIABLES
The Pure and Applied Mathematics, 2016 Abstract. We give representations of difierential operators and rules for additionand multiplication of dual quaternions. Also, we research the notions and propertiesof a regular function and a corresponding harmonic function with values in dualquaternions of Clifiord analysis. 1.
JI EUN KIM, KWANG HO SHON
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Functional Calculus for Dual Quaternions
Advances in Applied Clifford Algebras, 2023 We give a formula for $f(η)$, where $f :\mathbb C \to \mathbb C$ is a continuously differentiable function satisfying $f(\bar z) = \overline{f(z)}$, and $η$ is a dual quaternion. Note this formula is straightforward or well known if $η$ is merely a dual number or a quaternion.
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