Transformation Of Cartesian Coordinates Research Articles

An Integrated Scheme of the Data-Driven Multi-Block FCMs for Modeling the Steady Turning Motion of Motorboats

The steady turning motion of merchant ships is modeled according to industry specifications. However, challenges arise when motorboats are modeled. This study proposes a novel data-driven multi-block fuzzy cognitive map (FCM) model trained based on sea trials with four ship states. The optimal positions sampled by two different types of sensors were modeled using inverse variance weighting, which takes both Cartesian coordinate transformation and the constraints of the locations of the apparatuses into consideration. Combining these samplings with a scheme of multi-block FCMs, we conducted a study on data from motorboat trials. Our results closely approximate the data from motorboat trials at sea and are validated by a generated dataset of the classical model. Furthermore, we reveal the characteristics of our scheme, including the number of data blocks, the boundary of each block, and the parameters of the FCM for each block. As opposed to the classical method, the proposed scheme is insensitive to speed. This study presents a promising step toward mining modeling information from ship trials.

A comparison between Fukushima-Halley algorithm and Trilateration algorithm for geodetic conversion

The geodetic transformation of Cartesian coordinates into their elliptical equivalent is a fundamental problem in geodesy. The Fukushima algorithm accelerated by Halley method (Fukushima-Halley) is considered the standard in this conversion. The Trilateration algorithm is a recent algorithm solving the conversion problem through a computational geometry approach. This study compared the Trilateration algorithm to the Fukushima-Halley algorithm in aspects of accuracy of results, time efficiency, and space efficiency. Also, the parallel version of both algorithms was established using the Master-Slave technique and compared. The Trilateration Algorithm showed a slightly higher accuracy compared to Fukushima-Halley algorithm, which allocated less space in memory, and was 2.6 faster in sequential version compared to 1.9 in the parallel version. The study introduced a benchmark for arithmetic operation on the testing machine to be used in time efficiency comparison.

A New Way for Cartesian Coordinate Transformation and Its Precision Evaluation

High-precision coordinate transformation is vital for high-quality data fusion involving different coordinate systems. The transformation precision is mainly evaluated by the transformation parameters’ estimation precision, the root mean square error (RMSE) of the conversion of common points, or the RMSE of the conversion of check points. However, there are a number of issues associated with the rotation parameters’ precision estimated by the existing transformation methods. First, the estimated precision is related to the rotation matrix, so it is not suitable for scenarios where different rotation matrices are used. Second, the RMSE of the conversion of check points may not be consistent with the RMSE of the conversion of common points, so that the RMSE of the conversion of common points should not be used as a transformation precision index. In addition, some engineering applications do not have check points, and many applications need to know which range of points can meet our requirements. To deal with these limitations, this paper proposes a new way to calculate the translation parameters and evaluate the transformation precision. A lot of experimental data was used to verify the effectiveness and applicability of the proposed transformation model.

Direct transformation from Cartesian into geodetic coordinates on a triaxial ellipsoid

This paper1 presents two new direct symbolic-numerical algorithms for the transformation of Cartesian coordinates into geodetic coordinates considering the general case of a triaxial reference ellipsoid. The problem in both algorithms is reduced to finding a real positive root of a sixth degree polynomial. The first approach consists of algebraic manipulations of the equations describing the geometry of the problem and the second one uses Gröbner bases. In order to perform numerical tests and accurately compare efficiency and reliability, our algorithms together with the iterative methods presented by M. Ligas (2012) and J. Feltens (2009) have been implemented in C++. The numerical tests have been accomplished by considering 10 celestial bodies, referenced in the available literature. The obtained results show that our algorithms improve the aforementioned, up-to-date reference, iterative methods, in terms of both efficiency and accuracy.

Trilateration algorithm to transform Cartesian coordinates into geodetic coordinates

The transformation of Cartesian coordinates (xp, yp, zp) of a point (P) into their geodetic equivalent (ϕ, λ, h) in reference to the geodetic ellipsoid, is an essential requirement in geodesy. There are many well-known algorithms solving this transformation in closed-form, approximate or iterative approaches. This paper presents a new algorithm named “Trilateration Algorithm” for this transformation. It is based on the new “Seta-Point Theorem” in the meridian plan, which defines a new deterministic Twin-Point (P0) for the point (P). From the Twin-Point (P0), a single iteration solution is processed to achieve highly-accurate values for (ϕ, h) in a relatively simple and deterministic computation algorithm which is valid and stable for all values of (ϕ, h). The proposed solution was tested on a sample of 4277 points that cover all possible cases of point (P). The produced maximum absolute error in latitude is (0.000 0026″) and (0.000 476 mm) in height, computed from first iteration.

Application of Variable Projection Method based on Gram-Schmidt Orthogonalization in Spatial Cartesian Coordinate Transformation Model

For the linear and nonlinear parameters that can be separated in the spatial Cartesian coordinate transformation model, we use the variable projection algorithm in this paper to represent the linear parameters with nonlinear parameters, which are transformed into least squares problems with only nonlinear parameters. We simplify the matrix of the nonlinear function by the Gram-Schmidt orthogonalization method, and combine the nonlinear least squares iterative method with the Levenberg-Marquardt (LM) algorithm to solve for the coordinate transformation parameters. Experiments are carried out by solving for the coordinate transformation parameters of the independent spatial Cartesian coordinate system and the CGCS2000 coordinate system. We compare the solution results of the four methods (parameter non-separation method, traditional variable projection method, variable projection method based on QR decomposition, and variable projection method based on Gram-Schmidt orthogonal decomposition) with respect to the calculated results, the number of iterations and the computation time. The experimental results show that the proposed method in this paper requires a lower computation time and achieves higher computational efficiency when obtaining the same solution results and with the same number of iterations.

ColiCoords: A Python package for the analysis of bacterial fluorescence microscopy data.

Single-molecule fluorescence microscopy studies of bacteria provide unique insights into the mechanisms of cellular processes and protein machineries in ways that are unrivalled by any other technique. With the cost of microscopes dropping and the availability of fully automated microscopes, the volume of microscopy data produced has increased tremendously. These developments have moved the bottleneck of throughput from image acquisition and sample preparation to data analysis. Furthermore, requirements for analysis procedures have become more stringent given the demand of various journals to make data and analysis procedures available. To address these issues we have developed a new data analysis package for analysis of fluorescence microscopy data from rod-like cells. Our software ColiCoords structures microscopy data at the single-cell level and implements a coordinate system describing each cell. This allows for the transformation of Cartesian coordinates from transmission light and fluorescence images and single-molecule localization microscopy (SMLM) data to cellular coordinates. Using this transformation, many cells can be combined to increase the statistical power of fluorescence microscopy datasets of any kind. ColiCoords is open source, implemented in the programming language Python, and is extensively documented. This allows for modifications for specific needs or to inspect and publish data analysis procedures. By providing a format that allows for easy sharing of code and associated data, we intend to promote open and reproducible research. The source code and documentation can be found via the project’s GitHub page.

КОНХОІДАЛЬНЕ ПЕРЕТВОРЕННЯ, ЯК ПРИКЛАД АКТИВНОГО ПЕРЕТВОРЕННЯ КООРДИНАТ ПРИ ДИСКРЕТНОМУ МОДЕЛЮВАННІ ПОВЕРХОНЬ

The work discusses the possibilities of using active coordinate transformation using the example the Conchoidal transformation of space. There are many ways to form curved surfaces of different shapes. Transformation already well know and studied the geometrical objects is the most versatile way to obtain new curves of lines or surfaces. Synthesis of static-geometric method and geometric transformations will allow obtaining new forms of discrete models of various architectural surfaces. The selection of a geometric transformation is related to the original data of the simulated surface and the properties of the transformation itself. This approach will extend the list of design and aesthetic properties that can be considered in surface modeling. The conversion of discrete wireframes is one example of the generalization of the static-geometric method. The coordinates of the nodes of the discrete frame of the surface are determined without taking into account the external form-building loading on the nodes. This allows you to define the boundaries of the existence of discrete framework nodes in a layer between two boundary surfaces. Such surfaces, in shape, act as prototypes for new surfaces that are modeled. From a constructive point of view, boundary surfaces result from the selected spatial transformation of two planes. The formation of a discrete surface framework within the selected layer allows the shape of the simulated surface to be brought closer to the desired image, as evidenced by numerous examples. The main idea of the presented work is to demonstrate the possibilities of using spatial conchoidal transformation of Cartesian coordinates into spherical coordinates when forming discrete frameworks. Using this kind of conchoidal transformation together with the static-geometric method, when forming discrete images in three-dimensional point space, it is possible to obtain a surface whose appearance will be similar to the surface of revolution with a generatrix in the form the Сonhoid of Nycomed’s. Keywords: geometrical modeling, transformation of space, active transformation of coordinates, spatial conchoidal transformation, properties of transformation.

Increasing numerical efficiency of iterative solution for total least-squares in datum transformations

Cartesian coordinate transformation between two erroneous coordinate systems is considered within the Errors-In-Variables (EIV) model. The adjustment of this model is usually called the total Least-Squares (LS). There are many iterative algorithms given in geodetic literature for this adjustment. They give equivalent results for the same example and for the same user-defined convergence error tolerance. However, their convergence speed and stability are affected adversely if the coefficient matrix of the normal equations in the iterative solution is ill-conditioned. The well-known numerical techniques, such as regularization, shifting-scaling of the variables in the model, etc., for fixing this problem are not applied easily to the complicated equations of these algorithms. The EIV model for coordinate transformations can be considered as the nonlinear Gauss-Helmert (GH) model. The (weighted) standard LS adjustment of the iteratively linearized GH model yields the (weighted) total LS solution. It is uncomplicated to use the above-mentioned numerical techniques in this LS adjustment procedure. In this contribution, it is shown how properly diminished coordinate systems can be used in the iterative solution of this adjustment. Although its equations are mainly studied herein for 3D similarity transformation with differential rotations, they can be derived for other kinds of coordinate transformations as shown in the study. The convergence properties of the algorithms established based on the LS adjustment of the GH model are studied considering numerical examples. These examples show that using the diminished coordinates for both systems increases the numerical efficiency of the iterative solution for total LS in geodetic datum transformation: the corresponding algorithm working with the diminished coordinates converges much faster with an error of at least 10-5 times smaller than the one working with the original coordinates.

Fitting high-dimensional potential energy surface using active subspace and tensor train (AS+TT) method.

This paper is the first application of the tensor-train (TT) cross approximation procedure for potential energy surface fitting. In order to reduce the complexity, we combine the TT-approach with another technique recently introduced in the field of numerical analysis: an affine transformation of Cartesian coordinates into the active subspaces where the PES function has the most variability. The numerical experiments for the water molecule and for the nitrous acid molecule confirm the efficiency of this approach.

Kinematics Modelling and Simulation of Aero-Engine Fuel Piston Pump

Kinematics parameters calculation is the basis of piston pump design and performance analysis. Taking an axial piston pump with incline piston and spherical swash plate as the research object, Aimed at the deficiency of current formula for calculating piston pump kinematics parameters which included displacement, velocity and acceleration. In this paper, according to piston pump part motion geometry relationship, a correction kinematics algorithm is deduced by using the the spherical coordinate and cartesian coordinate transformation method, the analyse method and deduction procedure ensure the new calculating formula are precise in theory. Applying the calculating formula to an aero engine fuel axial piston pump, results show that. The displacement, velocity, acceleration according to the kinematics principle of piston pump, it can be used in the kind of piston pump kinematics parameters calculation and current calculating method evaluation.

Coordenadas cartesianas x coordenadas geológicas em geoestatística: aplicação à variável vagarosidade obtida por perfilagem acústica

O planejamento da lavra de um depósito mineral envolve o conhecimento de um ou mais atributos desse depósito. Esse conhecimento é obtido através de amostras do atributo em certos locais do depósito. Contudo a coleta de amostras pode envolver elevados custos, o que restringe o número de amostras e os locais onde valores do atributo são conhecidos. Assim, a estimativa de valores, em locais não amostrados, se torna necessária. A idéia de estimar valores em grids tridimensionais, utilizando amostras em coordenadas cartesianas e algoritmos da geoestatística pode levar a estimativas equivocadas em certas situações. Comumente, esse tipo de coordenadas não é compatível com a aplicação da geoestatística, visto que esse tipo de coordenadas pode prejudicar a determinação da continuidade dos valores amostrais e essa continuidade é a base dos algoritmos geoestatísticos. Assim, a questão da transformação de coordenadas cartesianas para coordenadas que permitam uma melhor determinação da continuidade dos valores amostrais é abordada nesse artigo. Para exemplificar a metodologia, uma transformação de coordenadas em um caso real de estimativas do atributo vagarosidade de onda acústica é apresentado.

Transforming Cartesian Coordinates X, Y, Z to Geographical Coordinates φ, λ, h

In November 1994, the Intergovernmental Committee on Surveying and Mapping (ICSM) adopted a new geodetic datum for Australia and recommended its progressive implementation nationally. This datum, designated Geocentric Datum of Australia (GDA) - compatible with the Global Positioning System (GPS), a US Department of Defense satellite positioning system - will eventually replace the existing Australian Geodetic Datum (AGD). Consequently, “old” AGD coordinates need to be converted to “new” GDA coordinates, which may require the transformation of Cartesian coordinates X,Y,Z to geographical coordinates φ, λ, h (latitude, longitude, height) related to an ellipsoid of revolution. Given X,Y,Z, longitude is easily derived, but not so latitude, which requires more sophisticated evaluation - usually by iterative techniques, or complicated direct methods - the height following readily once latitude is obtained. Thus Cartesian-to-geographic transformations revolve around the determination of latitude; this paper revie...

On the covariance of first-order differential systems

The transformation law for a first-order differential system under Cartesian-coordinate transformation is deduced and the concept of the relevant symmetry group is made precise. Also, it is proved that both the conservative structure and hyperbolicity of a system are preserved. The case of linear elasticity is examined in details.

Computer-aided three-dimensional reconstructions of the arrangement of primary spermatocytes in human seminiferous tubules.

With the use of a digital image-processing method three-dimensional reconstructions of the arrangement of spermatocytes in human seminiferous tubules were performed. With this method it was possible to investigate the cellular distribution in the tubule in nearly any given perspective and projection. In addition, by means of simple mathematical procedures, such as by transformation of Cartesian coordinates into cylindrical coordinates, it was possible to vary the shape of a reconstruction, i.e., to convert the cylindrical image of a tubular portion into a right-angled r-phi-z-representation. The present work not only confirms the existence of a complex helical plan of organization of the human seminiferous epithelium but also provides further aspects of the phenomenon of physiological germ-cell loss and its integration into the kinetics of spermatogenesis.

A new numerical method for collinear quantum reactive scattering using delves' coordinates: application to the H + H2(n ⩽ 7) → H2(m ⩽ 7) + H reaction

A new numerical method for quantum collinear chemical reactions using Delves' coordinates is described. the method used R-matrix propagation along the radial coordinate and a Delves'—cartesian coordinate transformation for the R matrix in the asymptotic region. Application is made to the H + H2(n ⩽ 7) → H2(m ⩽ 7) + H reaction.