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Journal articles on the topic 'Rectangular coordinate system'

Author: Grafiati

Published: 7 June 2025

Last updated: 16 July 2025

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1

Rudnicki, Mark, and Thomas H. Meyer. "Methods to Convert Local Sampling Coordinates into Geographic Information System/Global Positioning Systems (GIS/GPS)–Compatible Coordinate Systems." Northern Journal of Applied Forestry 24, no. 3 (2007): 233–38. http://dx.doi.org/10.1093/njaf/24.3.233.

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Abstract Laying out a sampling transect in the field is a common task when researching natural systems and resources. With widespread availability of global navigation satellite systems (GNSS), such as the US global positioning system (GPS), it is becoming more common to resurvey legacy transects to establish them in globally referenced coordinate systems such as geodetic latitude/longitude or planimetric systems such as the Universal Transverse Mercator (UTM) or the State Plane Coordinate System (SPCS). Transforming local coordinates into a globally referenced coordinate system allows (1) dis

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2

Shanurov, G. A., and A. D. Manilova. "Mobile scanning complex positioning accuracy depending on the coordinate systems used." Geodesy and Cartography 919, no. 1 (2017): 13–17. http://dx.doi.org/10.22389/0016-7126-2017-919-1-13-17.

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Inertial coordinate system and geodetic (terrestrial) coordinate system are used in processing of results of topographic survey, carried out with a mobile scanning complex. Mobile scanning complex geodetic coordinates, in turn, are presented in geodetic three-dimensional rectangular coordinate system form, in geodetic ellipsoidal coordinate system form and in the form of coordinates on a geodetic projection plane. The results of research, carried out earlier [4–7], suggest that the coordinate transformation on large areas distorts geodetic points coordinates. The article presents the results o

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3

Wang, Shu Ying, Zhan Min Yang, and Yi Wang. "A Range of Involute (Evolute) Transformation Model of Gear Characteristic Curve under Scroll Coordinate System." Advanced Materials Research 505 (April 2012): 494–500. http://dx.doi.org/10.4028/www.scientific.net/amr.505.494.

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By tangent and normal use of the circle scroll coordinate system is defined. Through regular, long pieces, short pieces of involute (evolute) process analysis, a range of involute (evolute) transformation model is established to achieve the high degree unity of a rectangular coordinate curves and polar coordinates (rotation) curve. For the practical application of engineering technology, the paper presented a method of continuous circular gear tooth profile curve, non-circular section of the conjugate gear involute curve rate curve for the rectangular coordinate, providing an effective way for

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4

Sokolova, L. "K. Polke's Theorem in Computer Model Space in 2D Modeling." Geometry & Graphics 12, no. 1 (2024): 12–21. http://dx.doi.org/10.12737/2308-4898-2024-12-1-12-21.

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The application of Polke's theorem in the search for a coordinate system for an electronic geometric model in the model space of a computer in 2D geometric modeling is considered. The possibility of creating an electronic geometric model in a system of axonometric axes in 2D modeling for scientific and educational purposes using a coordinate method is shown. It is possible to solve problems on axonometric coordinate planes that do not provide solutions in a rectangular coordinate system. In the computer model space, it has become possible to solve classical problems of descriptive geometry, th

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Khokhlov, Mikhail, and Olga Pozdnyakova. "The impact of system nonlinearities in the problem of optimal PMU placement for power system state estimation." E3S Web of Conferences 216 (2020): 01041. http://dx.doi.org/10.1051/e3sconf/202021601041.

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In PMU-based state estimation, a linear measurement model with phasors of both state variables and measurements expressed in rectangular coordinates has proven efficiency. The rectangular coordinate formulation is also used in optimal PMU placement problem aimed at providing the power system state estimation with the most informative measurements. In this case, it is assumed that the linearity of the measurement model ensures the optimality of the found placement of PMUs for any steady-state operating condition of the power system. The results presented in this paper show that this is not the

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6

Dong, Guo Jun, Cheng Shun Han, and Shen Dong. "Solution for Best Fitting Spherical Curvature Radius and Asphericity of Off-Axis Aspherics of Optical Aspheric Surface Component." Key Engineering Materials 364-366 (December 2007): 499–503. http://dx.doi.org/10.4028/www.scientific.net/kem.364-366.499.

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This study aimed to establish the coordinate transformation between the off-axis aspherics coordinate system σ and the axial symmetry aspherics coordinate system σ by transforming coordinates and present the computation models of asphericity in rectangular coordinate system and cylindrical coordinate system respectively. The asphericity expressions in both coordinate systems were applicable to the comparative sphere calculation of Off-axis aspherics with different figures. We selected an Initiation sphere in view of technology, along with equations in a right coordinate system for certain cali

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Sorokin, N. A. "Earth's gravity field parameters determination by the space geodesy dynamical approach." Geodesy and Cartography 919, no. 1 (2017): 7–12. http://dx.doi.org/10.22389/0016-7126-2017-919-1-7-12.

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The method of the geopotential parameters determination with the use of the gradiometry data is considered. The second derivative of the gravitational potential in the correction equation on the rectangular coordinates x, y, z is used as a measured variable. For the calculated value of the measured quantity required for the formation of a free member of the correction equation, the the Cunningham polynomials were used. We give algorithms for computing the second derivatives of the Cunningham polynomials on rectangular coordinates x, y, z, which allow to calculate the second derivatives of the

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8

Kluykov, A. A. "Technology of determining the Earth’s gravitational field parameters using gradiometric measurements Part 6. Calculation the components of the gravitational potential tensor in the earth’s spatial rectangular coordinate system." Geodesy and Cartography 973, no. 7 (2021): 2–8. http://dx.doi.org/10.22389/0016-7126-2021-973-7-2-8.

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This is the sixth one in a series of articles describing the technology of determining the Earth’s gravitational field parameters through gradiometric measurements performed with an onboard satellite electrostatic gradiometer. It provides formulas for calculating the components of the gravitational potential tensor in a geocentric spatial rectangular earth coordinate system in order to convert them into a gradiometric one and obtain a free term for the equations of correcting gradiometric measurements when determining the parameters of the Earth’s gravitational field. The components of the gra

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9

Li, Xiao Jie, and Bao Zhen Ge. "Correction of World Coordinate Error in the Three-Dimensional Laser Scanning System of Human Body." Applied Mechanics and Materials 198-199 (September 2012): 1016–20. http://dx.doi.org/10.4028/www.scientific.net/amm.198-199.1016.

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This paper studies three-dimensional laser scanning system of human body, and make adjustments according to the world coordinate error correction based on the point cloud obtained. This paper also analyzed the cause and characteristics of three-dimensional laser scanning system’s world coordinates error, and established the world coordinate correction model on the condition that vertical column coordinate error is not included in the calibration plane and the error is minimum relative to other highly cross-section. With a standard rectangular timber as the scan objects, correction factor is fi

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10

Kovalov, Sergiy, Svitlana Botvinovska, and Alla Zolotova. "ACTIVE TRANSFORMATION OF PLANES DURING FORMATION OF DISCRETE FRAMES WHITH A STATIC-GEOMETRIC METHOD." APPLIED GEOMETRY AND ENGINEERING GRAPHICS, no. 104 (February 4, 2025): 100–110. https://doi.org/10.32347/0131-579x.2023.104.100-110.

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Various transformations have found widespread use in applied geometry problems in simulating discrete frameworks of different surfaces with given properties. The paper presents a mathematical apparatus of active coordinate transformation, designed to solve problems of discrete geometric modeling. Under the active transformation of coordinates, the authors propose to consider a clear match between the points of the original and new coordinate systems, while maintaining their numerical correspondence, when the numerical values of the parameters of the original coordinate system will transition t

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Arjun, Tan. "From the Pear-shape of the Earth to a Tetrahedroid-shape of the Earth." APPLIED SCIENCE PERIODICAL XXVI, no. 4, November 2024 (2024): 15–23. https://doi.org/10.5281/zenodo.14802427.

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              <em>The notion of the ‘Pear-shape of the Earth’ is widely known to the public at large. However, a similar concept called the ‘Tetrahedroid-shape of the Earth’, is not. This concept was recently revived by Mentock, who argued that the tetrahedroid Earth was more appropriate than the pear-shaped Earth. In this study, we construct three model orientations of the tetrahedron within a circumscribed spherical Earth to see which orientation best locates the geoid highs with its four vertices. In the first model (Model A), one v

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Banachowicz, Andrzej, and Adam Wolski. "Determination of Ship Approach Parameters in the Polar Coordinates System." Reports on Geodesy and Geoinformatics 96, no. 1 (2014): 1–8. http://dx.doi.org/10.2478/rgg-2014-0001.

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Abstract An essential aspect of the safety of navigation is avoiding collisions with other vessels and natural or man made navigational obstructions. To solve this kind of problem the navigator relies on automatic anti-collision ARPA systems, or uses a geometric method and makes radar plots. In both cases radar measurements are made: bearing (or relative bearing) on the target position and distance, both naturally expressed in the polar coordinates system originating at the radar antenna. We first convert original measurements to an ortho-Cartesian coordinate system. Then we solve collision av

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Yan, Weitao, Junting Guo, Shaoge Yan, Yueguan Yan, and Wei Tang. "A Novel Surface Subsidence Prediction Model Based on Stochastic Medium Theory for Inclined Coal Seam Mining." Advances in Civil Engineering 2023 (December 2, 2023): 1–11. http://dx.doi.org/10.1155/2023/4640471.

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Most coal resources are deposited in the form of inclined coal seams, and surface subsidence basin morphology induced by the mining of inclined coal seams is frequently skewed. The probability integral method with symmetrical distribution characteristics is widely used at present in surface subsidence prediction in coal mining in China. However, this method performs poorly when the inclined coal seam mining subsidence is predicted, and prediction accuracy decreases considerably with an increase in coal seam inclination. To solve this problem, this study first establishes three coordinate syste

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14

Kilner, Steven J., and David L. Farnsworth. "Parabolic coordinates." Mathematical Gazette 105, no. 563 (2021): 226–36. http://dx.doi.org/10.1017/mag.2021.51.

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An important first step in understanding or solving a problem can be the selection of coordinates. Insight can be gained from finding invariants within a class of coordinate systems. For example, an important feature of rectangular coordinates is that the Euclidean distance between two points is an invariant of a change to another rectangular system by a rigid motion, which consists of translations, rotations and reflections. Indeed, the form of the distance function is an invariant. In calculus courses, students learn about polar coordinates, so that useful curves can be simply expressed and

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Zadorozhnaya, Irina, Igor Zaharov, and Andriy Tevyashev. "The measurement uncertainty of air object spatial coordinates by rho-theta fixing." Ukrainian Metrological Journal, no. 1 (March 31, 2022): 51–56. http://dx.doi.org/10.24027/2306-7039.1.2022.258821.

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The features of measurement uncertainty evaluation of the coordinates of an air object by the rho-theta fixing are discussed. Measurement models are presented that link its coordinates in the local rectangular coordinate system with the spherical coordinates of air object, found using a rangefinder and a goniometer. The models include a correction for determining the location of the base station, a correction for determining the angle of elevation due to inaccuracies in the leveling of the station platform and azimuth, and a correction related to the inaccuracy of the station’s reference to th

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Denih, Asep, Gustian Rama Putra, Zaqi Kurniawan, and Effendi Tri Bahtiar. "Developing a Model for Curve-Fitting a Tree Stem’s Cross-Sectional Shape and Sapwood–Heartwood Transition in a Polar Diagram System Using Nonlinear Regression." Forests 14, no. 6 (2023): 1102. http://dx.doi.org/10.3390/f14061102.

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A function from the domain (x-set) to the codomain (y-set) connects each x element to precisely one y element. Since each x-point originating from the domain corresponds to two y-points on the graph of a closed curve (i.e., circle, ellipse, superellipse, or ovoid) in a rectangular (Cartesian) diagram, it does not fulfil the function’s requirements. This non-function phenomenon obstructs the nonlinear regression application for fitting observed data resembling a closed curve; thus, it requires transforming the rectangular coordinate system into a polar coordinate system. This study discusses no

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17

Ben Slimane, Mourad, Moez Ben Abid, Ines Ben Omrane, and Mohamad Maamoun Turkawi. "Pointwise Rectangular Lipschitz Regularities for Fractional Brownian Sheets and Some Sierpinski Selfsimilar Functions." Mathematics 8, no. 7 (2020): 1179. http://dx.doi.org/10.3390/math8071179.

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We consider pointwise rectangular Lipschitz regularity and pointwise level coordinate axes Lipschitz regularities for continuous functions f on the unit cube I 2 in R 2 . Firstly, we provide characterizations by simple estimates on the decay rate of the coefficients (resp. leaders) of the expansion of f in the rectangular Schauder system, near the point considered. We deduce that pointwise rectangular Lipschitz regularity yields pointwise level coordinate axes Lipschitz regularities. As an application, we refine earlier results in Ayache et al. (Drap brownien fractionnaire. Potential Anal. 200

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18

Kroon, Cindy. "Back Page: My Favorite Lesson: Arctic Search and Destroy." Mathematics Teacher 108, no. 1 (2014): 80. http://dx.doi.org/10.5951/mathteacher.108.1.0080.

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“You sunk my battleship!”Many of us have fond memories of the Milton Bradley game Battleship®. Using rectangular coordinates to identify and sink an opponent's ships remains a classic childhood pastime. A similar activity can be used to help students as they learn to plot positions in the polar coordinate system. The Common Core State Standards for Mathematics (CCSSM) suggest that students “[r]epresent complex numbers on the complex plane in rectangular and polar form, and explain why the rectangular and polar forms of a given complex number represent the same number” (CCSSM Standard N-CN.4).

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19

Yang, Xue Wen, Zhi Quan Feng, Zhong Zhu Huang, and Na Na He. "A Gesture Recognition Algorithm Using Hausdorff-Like Distance Template Matching Based on the Main Direction of Gesture." Applied Mechanics and Materials 713-715 (January 2015): 2156–59. http://dx.doi.org/10.4028/www.scientific.net/amm.713-715.2156.

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Hand gesture of rotation, scaling and translation is the key problem of gesture recognition. This paper proposes a gesture recognition algorithm based on Hausdorff-like distance template matching of gesture main direction. Firstly, we segment hand gesture from video stream. Secondly, we calculate the main direction of gesture in the image, and build a 2D rectangular coordinate system. Then, we clockwise divide the gesture into eight sub-image area along the main direction of gesture and calculate the coordinates of target pixel points in each sub-image area in the 2D rectangular coordinate sys

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20

Botsiura, Olesia, Iryna Zadorozhna, and Igor Zakharov. "MEASUREMENT UNCERTAINTY EVALUATION OF OBJECT COORDINATES IN PLANE BY THE GONIOMETRIC METHOD." Metrology and instruments, no. 1 (November 29, 2024): 03. https://doi.org/10.30837/2663-9564.2024.1.03.

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The features of the uncertainty evaluation of measuring the coordinates of an object in plane by the goniometric method (theta position fixing) are discussed. Measurement model are presented that relate objects coordinates in the local rectangular coordinate system with the angles found using goniometers. The model includes corrections for determining the location of base stations, and correction associated with inaccuracies in the location of stations to the north. Uncertainty budgets for measurements of rectangular coordinates are given, which can be the basis for creating software for autom

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Carroll, William M. "Using a Polar Coordinate System in the Classroom." Arithmetic Teacher 37, no. 8 (1990): 42–45. http://dx.doi.org/10.5951/at.37.8.0042.

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Most elementary school students have experiences with a rectangular graphing system that helps to prepare them for ideas in algebra and analytic geometry. Mathematics books at the elementary school level contain a section on graphing, though it is often one of the later chapters, where it may be treated as supplementary material. In science and in social studies, students may find various data graphed or may have a project in which they have to graph daily temperatures, rainfall, or test scores. Biorhythms, record sales charts, or, for the more ambitious, the daily stock market give additional

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Xue, Ren Yong, and Ren Yi. "Proof of Goldbach Conjecture." Bulletin of Mathematical Sciences and Applications 7 (February 2014): 1–8. http://dx.doi.org/10.18052/www.scipress.com/bmsa.7.1.

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This paper through the creation of "double rectangular coordinate system", within the I quadrants, each coordinate axis coordinates all constitute the infinite sets. Coordinates with infinite sets one toone correspondence between the elements within and equal relationship. With any of the sum of two odd prime Numbers (a + b) to form a square area, length for a quarter of a square area A1 "square" diagonal integration method, a quarter of a square area A1 equation is derived with the definite integral equation; A1 area value of the argument as infinite generalized integral value, and deduce the

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Li, Chuan Xin. "Two Equivalent Reduction Methods of Dielectric Constant Tensor for Hexagonal Crystal System Materials." Key Engineering Materials 837 (April 2020): 146–52. http://dx.doi.org/10.4028/www.scientific.net/kem.837.146.

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Hexagonal crystal system materials have very important applications in modern society. Dielectric constant tensor of hexagonal crystal system materials is simplified only by the formula in a hexagonal coordinate system, not by the formula often seen in current Chinese solid state physics textbooks. Meanwhile, the equivalence of hexagonal coordinate system and rectangular coordinate system is presented in the paper.

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Medvedev, P. A., and M. V. Novgorodskaya. "Development of mathematical model Gauss – Kruger coordinate system for calculating planimetric rectangular coordinates using geodesic coordinates." Geodesy and Cartography 926, no. 8 (2017): 10–19. http://dx.doi.org/10.22389/0016-7126-2017-926-8-10-19.

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Algorithms with improved convergence for the calculation of rectangular coordinates in the Gauss – Kruger coordinate system according to the parameters of any ellipsoid were designed. The approach of definition the spherical components in the classic series defined variables x, y, represented by the difference between the degrees of longitude l, followed by the replacement of their sums by formulas of spherical trigonometry. For definition of the amounts of spherical components of the relevant decompositions patterns of transverse-cylindrical sphere plane projection in the condition of the ini

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Li, Xiaofei, Dongyan Zhao, Haosen Zhai, Mingdong Chen, and Tian Zhang. "Modal analysis of circular arches in rectangular coordinate system." Structures 47 (January 2023): 2129–37. http://dx.doi.org/10.1016/j.istruc.2022.12.036.

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Dzhenzher, V. O., and L. V. Denisova. "SCIENTIFIC GRAPHICS IN PASCALABC.NET: PLOTTING FUNCTION GRAPHS IN A RECTANGULAR CARTESIAN COORDINATE SYSTEM." Informatics in school, no. 1 (March 11, 2020): 31–39. http://dx.doi.org/10.32517/2221-1993-2020-19-1-31-39.

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The article considers the algorithm for plotting functions in a rectangular Cartesian coordinate system. A method is described for converting coordinates from a natural system to a screen system. The algorithm is implemented in the programming language PascalABC.NET. The necessary information about the graphical tools of the language is presented, the program code with detailed explanations is given. A distinctive feature of the method is the use of visual and easily calculated parameters for scaling the graph.

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Kluykov, A. A., and S. N. Yashkin. "Computation of first and second order derivatives gravity potential in different coordinate systems." Geodesy and Cartography 925, no. 7 (2017): 15–22. http://dx.doi.org/10.22389/0016-7126-2017-926-8-15-22.

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The determination of parameters of the Earth’s gravitational field model by using the satellite gravity projects CHAMP, GRACE, GOCE is carried out on the basis of mathematical processing of measurement information of sensor systems installed on board of a spacecraft. Each of these sensor systems realizes its coordinate system, in which measurements are performed. Measured parameters, as a rule, are related to the coordinate system of the sensory system, and the required parameters refer to the Earth’s coordinate system (EFRF). Therefore, to determine the required parameters, it is necessary to

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IUKHNO, Alona, Dmytro SOPOV, and Dmytro HOPTSII. "PERFORMANCE OF ENGINEERING SURVEYS AS AN INTEGRAL PART OF LAND AND CADASTRE WORKS IN PREPARATION OF LAND PLOTS FOR REGISTRATION IN THE BASE OF THE STATE LAND CADASTER." Ukrainian Journal of Applied Economics 6, no. 3 (2021): 273–80. http://dx.doi.org/10.36887/2415-8453-2021-3-37.

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Performing engineering surveys is a mandatory part of the development of technical documentation on land management. Surveys allow to confirm the accuracy of the performed geodetic or topographic survey. In particular, the accuracy of determining the geodetic coordinates of the turning points of the boundaries of the land, to link the turning points of the boundaries of the land to the geodetic points of the State Geodetic Network of Ukraine. The main purpose of the article is to reflect the main components of engineering surveys as part of land cadastral works in preparation of land for regis

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Khomasuridze, N. "Effective Solution of a Class of Boundary Value Problems of Thermoelasticity in Generalized Cylindrical Coordinates." gmj 11, no. 3 (2004): 495–514. http://dx.doi.org/10.1515/gmj.2004.495.

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Abstract A class of static boundary value problems of thermoelasticity is effectively solved for bodies bounded by coordinate surfaces of generalized cylindrical coordinates ρ, α, 𝑧 (ρ, α are orthogonal curvilinear coordinates on the plane and 𝑧 is a linear coordinate). Besides in the Cartesian system of coordinates some boundary value thermoelasticity problems are separately considered for a rectangular parallelepiped. An elastic body occupying the domain Ω = {ρ 0 < ρ < ρ 1, α 0 < α < α 1, 0 < 𝑧 < 𝑧1}, is considered to be weakly transversally isotropic (the medium is weakly

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Wang, Qiang, Cong Li, Jia Jie Cui, Lai Wei Jiang, Meng Wang, and De Kai Lu. "Application Research of the Polynomial Fitting Model in Transformation of Plane Rectangular Coordinate." Applied Mechanics and Materials 571-572 (June 2014): 143–47. http://dx.doi.org/10.4028/www.scientific.net/amm.571-572.143.

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Since the earth is a spheroid, the coordinate systems of different countries are not the same. And because China is a vast country, many places in China also established an independent coordinate system. In the application of engineering, the transformation between different rectangular coordinate is very necessary. This paper studies the function model that polynomial fitting model of rectangular coordinate transformation, and explored the rule of impact on the accuracy that between different fitting models and the numbers of common points selected in the same model using real data. Finally,

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Morgaś, Wacław, and Zdzisław Kopacz. "Conversion of geodetic coordinates into flat (2-dimensinal) coordinates PL-UTM for the purposes of navigation." Zeszyty Naukowe Akademii Marynarki Wojennej, no. 1 (March 31, 2017): 45–60. http://dx.doi.org/10.5604/0860889x.1237622.

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This paper presents mathematical interdependences in converting geodetic coordinates into flat rectangular coordinates and inverse transformation recommended in the Ordinance by Prime Minister on the State System of Spatial References. It especially presents formulas contained in works by M. Hooijberg (1997) Practical Geodesy and R. Kadaj (2001) Projection Formulas and Parameters of Coordinate Systems. G-1.10.In order to illustrate uses of the presented formulas relevant calculation examples based on the reference ellipsoids WGS 84 and GRS 80 are included.

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Киричук, Юрій Володимирович. "Mean-square errors of object positioning in rectangular coordinate system." Technology audit and production reserves 1, no. 4(15) (2014): 21. http://dx.doi.org/10.15587/2312-8372.2014.21694.

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HONG, QINGQUAN. "POWER-FLOW DENSITY OF ELECTRIC QUADRUPOLE RADIATION IN MAGNETIC ANISOTROPIC MEDIUM." International Journal of Modern Physics B 22, no. 03 (2008): 239–45. http://dx.doi.org/10.1142/s0217979208038569.

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The radium in anisotropic medium is investigated. A general formula is worked out for showing power-flow of electric quadrupole radiation with tensor form in anisotropic magnetic medium. After substituting the radiation field of electric quadrupole into this general formula, an expression of average power-flow density electric quadrupole radium in anisotropic magnetic medium is then obtained at anisotropic rectangular coordinate system through dyadic calculation. After coordinate transformation, an expression of average power-flow density of electric quadrupole radium in anisotropic magnetic m

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Meng, Li, Xiaochong Tong, Shuaibo Fan, et al. "A Universal Generating Algorithm of the Polyhedral Discrete Grid Based on Unit Duplication." ISPRS International Journal of Geo-Information 8, no. 3 (2019): 146. http://dx.doi.org/10.3390/ijgi8030146.

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Based on the analysis of the problems in the generation algorithm of discrete grid systems domestically and abroad, a new universal algorithm for the unit duplication of a polyhedral discrete grid is proposed, and its core is “simple unit replication + effective region restriction”. First, the grid coordinate system and the corresponding spatial rectangular coordinate system are established to determine the rectangular coordinates of any grid cell node. Then, the type of the subdivision grid system to be calculated is determined to identify the three key factors affecting the grid types, which

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Abuhmaidan, Khaled, Monther Aldwairi, and Benedek Nagy. "Vector Arithmetic in the Triangular Grid." Entropy 23, no. 3 (2021): 373. http://dx.doi.org/10.3390/e23030373.

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Vector arithmetic is a base of (coordinate) geometry, physics and various other disciplines. The usual method is based on Cartesian coordinate-system which fits both to continuous plane/space and digital rectangular-grids. The triangular grid is also regular, but it is not a point lattice: it is not closed under vector-addition, which gives a challenge. The points of the triangular grid are represented by zero-sum and one-sum coordinate-triplets keeping the symmetry of the grid and reflecting the orientations of the triangles. This system is expanded to the plane using restrictions like, at le

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Jiang, Shuai, Lei Wang, and Yuanyuan Dong. "Application of Virtual Reality Human-Computer Interaction Technology Based on the Sensor in English Teaching." Journal of Sensors 2021 (November 19, 2021): 1–10. http://dx.doi.org/10.1155/2021/2505119.

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In order to improve the online English teaching effect, the paper applies the sensor and human-computer interaction into the English teaching. The paper improves the sensor information by applying Kalman Filter, combines sensor positioning algorithm to trace the students in the English teaching online, and turns the kernels by the skeleton algorithm into corresponding coordinates of space rectangular coordinate system taking the waist as a coordinate origin to get a human-computer interaction skeleton model in the virtual reality. According to the actual needs of English teaching human-compute

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Sanger, Terence D. "Theoretical Considerations for the Analysis of Population Coding in Motor Cortex." Neural Computation 6, no. 1 (1994): 29–37. http://dx.doi.org/10.1162/neco.1994.6.1.29.

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Recent evidence of population coding in motor cortex has led some researchers to claim that certain variables such as hand direction or force may be coded within a Cartesian coordinate system with respect to extra personal space. These claims are based on the ability to predict the rectangular coordinates of hand movement direction using a “population vector” computed from multiple cells' firing rates. I show here that such a population vector can always be found given a very general set of assumptions. Therefore the existence of a population vector constitutes only weak support for the explic

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Minnaert, Ben, Giuseppina Monti, and Mauro Mongiardo. "Unified Representation of 3D Multivectors with Pauli Algebra in Rectangular, Cylindrical and Spherical Coordinate Systems." Symmetry 14, no. 8 (2022): 1684. http://dx.doi.org/10.3390/sym14081684.

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In practical engineering, the use of Pauli algebra can provide a computational advantage, transforming conventional vector algebra to straightforward matrix manipulations. In this work, the Pauli matrices in cylindrical and spherical coordinates are reported for the first time and their use for representing a three-dimensional vector is discussed. This method leads to a unified representation for 3D multivectors with Pauli algebra. A significant advantage is that this approach provides a representation independent of the coordinate system, which does not exist in the conventional vector perspe

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Younes, J. A., and M. G. Mustafin. "The characteristics of transforming coordinates from the geocentric system WGS-84 for the Mercator projection under low latitudes conditions." Geodesy and Cartography 940, no. 10 (2018): 2–6. http://dx.doi.org/10.22389/0016-7126-2018-940-10-2-6.

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The issue of calculating the plane rectangular coordinates using the data obtained by the satellite observations during the creation of the geodetic networks is discussed in the article. The peculiarity of these works is in conversion of the coordinates into the Mercator projection, while the plane coordinate system on the base of Gauss-Kruger projection is used in Russia. When using the technology of global navigation satellite system, this task is relevant for any point (area) of the Earth due to a fundamentally different approach in determining the coordinates. The fact is that satellite de

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P.A., Medvedev, and Novorodskaya M.V. "Mathematical models of Gauss-Kruger coordinate system study aimed at calculating of geodetic coordinates by flat rectangular coordinates." Geodesy and Aerophotosurveying 63, no. 3 (2019): 264–74. http://dx.doi.org/10.30533/0536-101x-2019-63-3-264-274.

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Obidenko, V. I. "Prospects of using hybrid local coordinate systems based on SCS-2011." Geodesy and Cartography 998, no. 8 (2023): 2–12. http://dx.doi.org/10.22389/0016-7126-2023-998-8-2-12.

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The author presents the results of an experiment on the practical implementation of the methodology for creating a hybrid local coordinate system LCS_2011(95), based on SCS-2011, where flat rectangular coordinates coincide with similar ones in CS-95. The study was carried out in the Novosibirsk oblast, the territory of which is located within three 6° coordinate zones SCS-2011 (CS-95). It is shown that in order to create a LCS_2011(95) in a region that includes several such areas, it is required to use transformation algorithms adequate in terms of accuracy. The research confirmed high accurac

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Walton, Karen Doyle, and J. Doyle Walton. "Microcomputer-Assisted Mathematics: Computer-Assisted Polar Graphing." Mathematics Teacher 80, no. 3 (1987): 246–50. http://dx.doi.org/10.5951/mt.80.3.0246.

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Faced with the dilemma of how to teach polar coordinates? Whether the subject is being introduced at the secondary school or college level, the problem is the same. At either level, the objectives include the following; (1) introduce a new coordinate system, relating (x, y) rectangular coordinates to (r, Q) polar coordinates; (2) enable the students to plot polar equations; (3) acquaint students with standard types of polar graphs; and (4) find points of intersection of two polar graphs. This article presents a method of using the microcomputer to teach polar coordinates and graphing in an eff

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Karpyuk, L. V., N. O. Davydenko та Gezevi Abdalhaleh Goma Ahmed. "Аxonometric transformations of a complex drawing". Вісник Східноукраїнського національного університету імені Володимира Даля, № 1 (277) (10 березня 2023): 43–47. http://dx.doi.org/10.33216/1998-7927-2023-277-1-43-47.

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When drawing up technical drawings, it is sometimes necessary to have visual representations along with images of objects in the orthogonal projection system. For such images, the method of axonometric projection is used (axonometry is a Greek word, literally translated as measurement along the axes; axon means axis, metreo means measuring). The essence of the axonometric projection method: an object, together with the axes of rectangular coordinates to which it is assigned in space, is projected onto a certain plane so that none of its coordinate axes is projected onto it at a point. In this

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Duss' eaux, R., P. Chambelin, and C. Faure. "Analysis of Rectangular Waveguide H-Plane Junctions in Nonorthogonal Coordinate System." Progress In Electromagnetics Research 28 (2000): 205–29. http://dx.doi.org/10.2528/pier99092001.

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Kim, Tae Woo, Hong Sik Yun, Dong Ha Lee, Gun Soo Kim, and Young Chang Koh. "Establishment of New Single Origin Plane Rectangular Coordinate System in Korea." Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography 31, no. 3 (2013): 183–92. http://dx.doi.org/10.7848/ksgpc.2013.31.3.183.

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Zhang, Junhua, Wei Zhang, and Yuxin Hao. "Multipulse Chaotic Dynamics for Nonautonomous Nonlinear Systems and Application to a FGM Plate." International Journal of Bifurcation and Chaos 24, no. 05 (2014): 1450068. http://dx.doi.org/10.1142/s0218127414500680.

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The extended Melnikov method is improved to investigate the nonautonomous nonlinear dynamical system in Cartesian coordinate. The multipulse chaotic dynamics of a simply supported functionally graded materials (FGM) rectangular plate subjected to transversal and in-plane excitations is investigated in this paper for the first time. The formulas of the FGM rectangular plate are two-degree-of-freedom nonautonomous nonlinear system with coupling of nonlinear terms including several square and cubic terms. The extended Melnikov method is improved to enable us to analyze directly the nonautonomous

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Legkostup, V. V., and V. E. Markevich. "Methodology of determining of the transfer function of engagement kinematics of accelerations of an aircraft and its elliptic coordinates used for thr guidance based on time difference of arrival." «System analysis and applied information science», no. 1 (April 26, 2021): 12–20. http://dx.doi.org/10.21122/2309-4923-2021-1-12-20.

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This paper discusses the problem of determining a kinematics (in terms of transfer function, as far as possible) of parameters of the motion of an aircraft expressed in the curvilinear coordinate system and control accelerations expressed in a rectangular coordinate system. Examples of curvilinear coordinate systems using in practice can be polar, biangular, two-center bipolar, elliptic, parabolic cylindrical, spherical, ellipsoidal, coordinate systems. A technique for obtaining a kinematic link for the control problem of an unmanned aerial vehicle in the elliptic coordinate system was describ

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Simonyan, Vladimir V., and Alexey A. Kochiev. "Mathematical model of landslide stable equilibrium." Vestnik MGSU, no. 10 (October 2019): 1292–98. http://dx.doi.org/10.22227/1997-0935.2019.10.1292-1298.

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Introduction. A definition of landslide stability condition is given for any sliding surfaces, density, mass, volume, slope, i.e., in general. As a result of mathematical analysis, equilibrium equations in coordinates are obtained. When violating any of these conditions, the landslide movement begins. The problem is in the way of obtaining real parameter values entering the equations. The mechanical and mathematical model of a landslide having an arbitrary sliding surface is the subject of the study. The aim is determining a time of landslide movement beginning and central issues in the task o

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Lü, Fangcheng, Jiayi Guo, Leilei Niu, Jianghai Geng, and Yirui Pan. "A New 3D Method for Reactor Core Vibration Based on Silicon Steel Lamination Rules and Application in UHV Shunt Reactors." Mathematical Problems in Engineering 2019 (October 23, 2019): 1–11. http://dx.doi.org/10.1155/2019/7290536.

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A new three-dimensional (3D) analysis method is proposed as the existing two-dimensional (2D) method has low accuracy in analysing the vibration characteristics of oil-immersed shunt reactors, such as ultrahigh-voltage (UHV) shunt reactors. First of all, a set of 3D laminated coordinate systems was defined based on silicon steel lamination rules, in which the anisotropy of magnetic properties for laminated silicon steel in the rolling direction (RD), the transverse direction (TD), and the lamination direction (LD) were considered. Then, the mapping between laminated coordinate systems and spac

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Paramonov, A. A., and A. V. Kalach. "SIMULATION OF EMERGENCIES USING ALMOST PERIODIC ANALYSIS OF IMAGES OF TYPHOON STRUCTURE." Bulletin of the South Ural State University series "Mathematics. Mechanics. Physics" 16, no. 4 (2024): 67–74. https://doi.org/10.14529/mmph240408.

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The paper considers the method of transforming images from rectangular coordinate system to polar coordinate system for further near-periodic analysis of typhoon structure based on generalized shear function. The basic method of near-periodic analysis involves dividing the data into highfrequency oscillatory components and low-frequency trends based on the proportion theory, which can identify near-periodic characteristics. The paper shows that near-periodic analysis is applicable to both radius-vector and angle image data in a polar coordinate system. The practical component of the work is de

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