Results 21 to 30 of about 245 (169)

Geometric Algebra Applications in Geospatial Artificial Intelligence and Remote Sensing Image Processing

IEEE Access, 2020
With the increasing demand for multidimensional data processing, Geometric algebra (GA) has attracted more and more attention in the field of geographical information systems.
Uzair Aslam Bhatti, Zhaoyuan Yu, Linwang Yuan, Zeeshan Zeeshan, Saqib Ali Nawaz, Mughair Bhatti, Anum Mehmood, Qurat Ul Ain, Luo Wen   +8 more
doaj   +1 more source

Exponential and logarithm of multivector in low-dimensional (n = p + q < 3) Clifford algebras

Nonlinear Analysis, 2022
The aim of the paper is to give a uniform picture of complex, hyperbolic, and quaternion algebras from a perspective of the applied Clifford geometric algebra.
Adolfas Dargys, Artūras Acus
doaj   +1 more source

Exponentials of general multivector in 3D Clifford algebras

Nonlinear Analysis, 2022
Closed form expressions to calculate the exponential of a general multivector (MV) in Clifford geometric algebras (GAs) Clp;q are presented for n = p + q = 3.
Adolfas Dargys, Artūras Acus
doaj   +1 more source

UAV’s Agricultural Image Segmentation Predicated by Clifford Geometric Algebra

IEEE Access, 2019
Image segmentation is widely used in the field of agriculture to improve the yields and protecting them from pests, herbs, shrubs, and weeds. Precision agriculture is also contributing to the inter and intra crop monitoring.
Prince Waqas Khan, Guangxia Xu, Muhammad Ahsan Latif, Khizar Abbas, Ammara Yasin   +4 more
doaj   +1 more source

Computing in the Conformal Space Objects, Incidence Relations, and Geometric Constrains for Applications in AI, GIS, Graphics, Robotics, and Human-Machine Interaction

IEEE Access, 2022
This article presents a revisited proposal for the formulation of objects and geometric relations and constraints in the conformal space. For modeling, graphics engineering, kinematics, and dynamics, the solution of problems using only points and lines ...
Eduardo Jose Bayro-Corrochano, G. Altamirano-Escobedo, A. Ortiz-Gonzalez, V. Farias-Moreno, N. Chel-Puc   +4 more
doaj   +1 more source

Logarithm of multivector in real 3D Clifford algebras

Nonlinear Analysis, 2023
Closed form expressions for a logarithm of general multivector (MV) in basis-free form in real geometric algebras (GAs) Clp,q are presented for all n = p + q = 3.
Artūras Acus, Adolfas Dargys
doaj   +1 more source

Algebraic programming of geometrical calculus and clifford algebra

Journal of Symbolic Computation, 1989
The basic concepts of geometrical calculus have been implemented in an algebraic programming language. In this paper, we describe how our program performs fundamental operations on multivectors.
Ph. Tombal, A. Moussiaux
openaire   +2 more sources

Relativity in Clifford's Geometric Algebras of Space and Spacetime [PDF]

International Journal of Theoretical Physics, 2004
Of the various formalisms developed to treat relativistic phenomena, those based on Clifford's geometric algebra are especially well adapted for clear geometric interpretations and computational efficiency. Here we study relationships between formulations of special relativity in the spacetime algebra (STA) Cl{1,3} of Minkowski space, and in the ...
Baylis, William E., Sobczyk, Garret
openaire   +2 more sources

A new derivation of the Minkowski metric

Journal of Physics Communications, 2023
The four dimensional spacetime continuum, as first conceived by Minkowski, has become the dominant framework within which to describe physical laws.
James M Chappell, John G Hartnett, Nicolangelo Iannella, Azhar Iqbal, David L Berkahn, Derek Abbott   +5 more
doaj   +1 more source

Time as a geometric property of space

Frontiers in Physics, 2016
The proper description of time remains a key unsolved problem in science. Newton conceived of time as absolute and universal which it `flows equably without relation to anything external'}.
James Michael Chappell, John Gideon Hartnett, Nicolangelo Iannella, Azhar Iqbal, Derek Abbott   +4 more
doaj   +1 more source