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Relevant bibliographies by topics / Quaternion projections

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Academic literature on the topic 'Quaternion projections'

Author: Grafiati

Published: 4 June 2021

Last updated: 18 February 2022

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Journal articles on the topic "Quaternion projections"

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Xing, Yan, Jie Qing Tan, and Pei Lin Hong. "Perspective Projection Based on Quaternion Interpolation." Applied Mechanics and Materials 303-306 (February 2013): 2130–33. http://dx.doi.org/10.4028/www.scientific.net/amm.303-306.2130.

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Quaternion sandwiching formula to compute perspective projections has been given by Ron Goldman in an article titled “Understanding quaternions”. In this paper, we applied this method to obtain perspective images of 3D objects, and proposed a modified method to interpolate two projection planes with different directions and distances from eye point to acquire an intermediate viewing plane. Experimental results show that our interpolation method improves the disadvantage of uneven movement speed when quaternion SLERP method is directly adopted.

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Koca, Nazife Özdeş, Mehmet Koca, and Muna Al-Sawafi. "FCC, BCC and SC Lattices Derived from the Coxeter-Weyl groups and quaternions." Sultan Qaboos University Journal for Science [SQUJS] 19, no. 1 (2014): 95. http://dx.doi.org/10.24200/squjs.vol19iss1pp95-104.

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We construct the fcc (face centered cubic), bcc (body centered cubic) and sc (simple cubic) lattices as the root and the weight lattices of the affine extended Coxeter groups W(A3) and W(B3)=Aut(A3). It is naturally expected that these rank-3 Coxeter-Weyl groups define the point tetrahedral symmetry and the octahedral symmetry of the cubic lattices which have extensive applications in material science. The imaginary quaternionic units are used to represent the root systems of the rank-3 Coxeter-Dynkin diagrams which correspond to the generating vectors of the lattices of interest. The group el

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Tozzi, Arturo, James F. Peters, Norbert Jausovec, et al. "Nervous Activity of the Brain in Five Dimensions." Biophysica 1, no. 1 (2021): 38–47. http://dx.doi.org/10.3390/biophysica1010004.

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The nervous activity of the brain takes place in higher-dimensional functional spaces. It has been proposed that the brain might be equipped with phase spaces characterized by four spatial dimensions plus time, instead of the classical three plus time. This suggests that global visualization methods for exploiting four-dimensional maps of three-dimensional experimental data sets might be used in neuroscience. We asked whether it is feasible to describe the four-dimensional trajectories (plus time) of two-dimensional (plus time) electroencephalographic traces (EEG). We made use of quaternion or

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Chelnokov, Yu N., and A. V. Molodenkov. "Quaternion Algorithm for Initial Alignment of Strapdown INS Using the A. N. Tikhonov Regularization Method." Mekhatronika, Avtomatizatsiya, Upravlenie 22, no. 4 (2021): 217–24. http://dx.doi.org/10.17587/mau.22.217-224.

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For the functioning of algorithms of inertial orientation and navigation of strapdown inertial navigation system (SINS), it is necessary to conduct a mathematical initial alignment of SINS immediately before the operation of these algorithms. An efficient method of initial alignment (not calibration!) of SINS is the method of vector matching. Its essence is to determine the relative orientation of the instrument trihedron Y (related to the unit of SINS sensors) and the reference trihedron X according to the results of measuring the projections of at least two non-collinear vectors of the axes

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Valle, Marcos Eduardo, and Rodolfo Anibal Lobo. "Quaternion-valued recurrent projection neural networks on unit quaternions." Theoretical Computer Science 843 (December 2020): 136–52. http://dx.doi.org/10.1016/j.tcs.2020.08.033.

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Ghiloni, Riccardo, Valter Moretti, and Alessandro Perotti. "Spectral representations of normal operators in quaternionic Hilbert spaces via intertwining quaternionic PVMs." Reviews in Mathematical Physics 29, no. 10 (2017): 1750034. http://dx.doi.org/10.1142/s0129055x17500349.

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The possibility of formulating quantum mechanics over quaternionic Hilbert spaces can be traced back to von Neumann’s foundational works in the thirties. The absence of a suitable quaternionic version of spectrum prevented the full development of the theory. The first rigorous quaternionic formulation has started only in 2007 with the definition of the spherical spectrum of a quaternionic operator based on a quadratic version of resolvent operator. The relevance of this notion is proved by the existence of a quaternionic continuous functional calculus and a theory of quaternionic semigroups re

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Koca, Mehmet, Nazife Ozdes Koca, and Ramazan Koc. "Affine coxeter group Wa(A4), quaternions, and decagonal quasicrystals." International Journal of Geometric Methods in Modern Physics 11, no. 04 (2014): 1450031. http://dx.doi.org/10.1142/s0219887814500315.

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We introduce a technique of projection onto the Coxeter plane of an arbitrary higher-dimensional lattice described by the affine Coxeter group. The Coxeter plane is determined by the simple roots of the Coxeter graph I2(h) where h is the Coxeter number of the Coxeter group W(G) which embeds the dihedral group Dh of order 2h as a maximal subgroup. As a simple application, we demonstrate projections of the root and weight lattices of A4 onto the Coxeter plane using the strip (canonical) projection method. We show that the crystal spaces of the affine Wa(A4) can be decomposed into two orthogonal

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Kobayashi, Masaki. "Storage Capacity of Quaternion-Valued Hopfield Neural Networks With Dual Connections." Neural Computation 33, no. 8 (2021): 2226–40. http://dx.doi.org/10.1162/neco_a_01405.

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A complex-valued Hopfield neural network (CHNN) is a multistate Hopfield model. A quaternion-valued Hopfield neural network (QHNN) with a twin-multistate activation function was proposed to reduce the number of weight parameters of CHNN. Dual connections (DCs) are introduced to the QHNNs to improve the noise tolerance. The DCs take advantage of the noncommutativity of quaternions and consist of two weights between neurons. A QHNN with DCs provides much better noise tolerance than a CHNN. Although a CHNN and a QHNN with DCs have the samenumber of weight parameters, the storage capacity of proje

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LEO, S. DE, and P. ROTELLI. "QUATERNION HIGGS AND THE ELECTROWEAK GAUGE GROUP." International Journal of Modern Physics A 10, no. 30 (1995): 4359–70. http://dx.doi.org/10.1142/s0217751x95002011.

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We show that, in quaternion quantum mechanics with a complex geometry, the minimal four Higgs of the unbroken electroweak theory naturally determine the quaternion invariance group which corresponds to the Glashow group. Consequently, we are able to identify the physical significance of the anomalous Higgs scalar solutions. In addition, we introduce and discuss the complex projection of the Lagrangian density.

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Kobayashi, Masaki. "Bicomplex Projection Rule for Complex-Valued Hopfield Neural Networks." Neural Computation 32, no. 11 (2020): 2237–48. http://dx.doi.org/10.1162/neco_a_01320.

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A complex-valued Hopfield neural network (CHNN) with a multistate activation function is a multistate model of neural associative memory. The weight parameters need a lot of memory resources. Twin-multistate activation functions were introduced to quaternion- and bicomplex-valued Hopfield neural networks. Since their architectures are much more complicated than that of CHNN, the architecture should be simplified. In this work, the number of weight parameters is reduced by bicomplex projection rule for CHNNs, which is given by the decomposition of bicomplex-valued Hopfield neural networks. Comp

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Dissertations / Theses on the topic "Quaternion projections"

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Dietrich, Franck. "Simulation numérique du couplage entre la mécanique du vol et l'aérodynamique des projectiles." Poitiers, 2003. http://www.theses.fr/2003POIT2319.

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L'étude du comportement en vol des projectiles met en œuvre des modèles de plus en plus réalistes prenant en compte la complexité multi-physique des phénomènes. L'objectif des travaux présentés est de sélectionner les méthodes numériques les mieux adaptées à la simulation numérique des phénomènes couplés d'aérodynamique et de mécanique du vol des projectiles " flèche " et gyrostabilisé. Pour cela, l'ensemble des méthodes existantes dans chacune des deux disciplines a été tout d'abord étudié en tenant compte des exigences du problème couplé. Puis, ces dernières ont été modifiées et adaptées pou

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Ochoa, Mayorga Victor Manuel. "Geometric approach to multi-scale 3D gesture comparison." Phd thesis, 2010. http://hdl.handle.net/10048/1530.

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The present dissertation develops an invariant framework for 3D gesture comparison studies. 3D gesture comparison without Lagrangian models is challenging not only because of the lack of prediction provided by physics, but also because of a dual geometry representation, spatial dimensionality and non-linearity associated to 3D-kinematics. In 3D spaces, it is difficult to compare curves without an alignment operator since it is likely that discrete curves are not synchronized and do not share a common point in space. One has to assume that each and every single trajectory in the space is unique

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Book chapters on the topic "Quaternion projections"

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Singh, Pushpendra, Pathik Sahoo, Komal Saxena, et al. "Quaternion, Octonion to Dodecanion Manifold: Stereographic Projections from Infinity Lead to a Self-operating Mathematical Universe." In Advances in Intelligent Systems and Computing. Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-5414-8_5.

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Schaeben, Helmut, and Ljudmila Meister. "Geometry of the ODF-to-PDF Projection in Quaternion Representation." In Materials Science Forum. Trans Tech Publications Ltd., 2005. http://dx.doi.org/10.4028/0-87849-975-x.283.

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Kabir, Kazi Lutful, Prasanna Venkatesh Parthasarathy, and Yash Tare. "Connecting Quaternion-Based Rotationally Invariant LCS to Pedestrian Path Projection." In Advances in Intelligent Systems and Computing. Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-33-4367-2_22.

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Xu, Zihan, Zhuhong Shao, Yuanyuan Shang, and Zhongshan Ren. "Full Quaternion Matrix and Random Projection for Bimodal Face Template Protection." In Biometric Recognition. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-86608-2_41.

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Boreskov, Alexey, and Evgeniy Shikin. "Transformations in 3D, projections, quaternions." In Computer Graphics. Chapman and Hall/CRC, 2013. http://dx.doi.org/10.1201/b14857-4.

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Conference papers on the topic "Quaternion projections"

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Purwar, Anurag, and Q. J. Ge. "Polar Decomposition of Unit Dual Quaternions." In ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/detc2012-70882.

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This paper seeks to extend the notion of polar decomposition from matrix algebra to dual quaternion algebra. The goal is to obtain a simple, efficient and explicit method for determining the polar decompositions (PD) of spatial displacements in Euclidean three-space that belong to a special Euclidean Group known as SE(3). It has been known that such a decomposition is equivalent to the projection of an element of SE(3) onto SO(4) that yields hyper spherical displacements that best approximate rigid-body displacements. It is shown in this paper that a dual quaternion representing an element of

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Valle, Marcos Eduardo, and Rodolfo Anibal Lobo. "An Introduction to Quaternion-Valued Recurrent Projection Neural Networks." In 2019 8th Brazilian Conference on Intelligent Systems (BRACIS). IEEE, 2019. http://dx.doi.org/10.1109/bracis.2019.00151.

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Reports on the topic "Quaternion projections"

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Maley, James M. Multiplicative Quaternion Extended Kalman Filtering for Nonspinning Guided Projectiles. Defense Technical Information Center, 2013. http://dx.doi.org/10.21236/ada588831.

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Amoruso, Michael J. Euler Angles and Quaternions in Six Degree of Freedom Simulations of Projectiles. Defense Technical Information Center, 1996. http://dx.doi.org/10.21236/ada417259.

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