A Comparison of Variational Projection and Cartographic Projection by Ritz’s Method
The application of alternative mathematical methods in creating cartographic projections is an interesting factor, which affects the optimization of distortions and their distribution in the projected territory. This article presents the methodology for the creation and comparison of conformal carto...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Sciendo
2022-06-01
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| Series: | Slovak Journal of Civil Engineering |
| Subjects: | |
| Online Access: | https://doi.org/10.2478/sjce-2022-0011 |
| _version_ | 1818502703865659392 |
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| author | Ábrahámová Andrea Vajsáblová Margita |
| author_facet | Ábrahámová Andrea Vajsáblová Margita |
| author_sort | Ábrahámová Andrea |
| collection | DOAJ |
| description | The application of alternative mathematical methods in creating cartographic projections is an interesting factor, which affects the optimization of distortions and their distribution in the projected territory. This article presents the methodology for the creation and comparison of conformal cartographic projections formed by alternative mathematical methods of minimizing the integral criterion for scale distortion in Slovakia. The creation of the variational projection is based on the Airy-Kavraiskii criterion of evaluating the projection on the displayed area by solving Laplace's equation. The second projection is created by solving Poisson's equation using Ritz's method. Our analysis showed that the variational projection of Slovakia achieves more satisfactory distortion values than the cartographic projection created using Ritz's method. The advantage of Ritz's method is that it is possible to choose a boundary condition for a predefined undistorted convex closed curve. In this paper, we have also derived specific members of the map equations for cartographic projection based on solving Poisson's equation by Ritz's method. |
| first_indexed | 2024-12-10T21:13:55Z |
| format | Article |
| id | doaj.art-ea014d3b1c6c4f7bae57933f5084eb86 |
| institution | Directory Open Access Journal |
| issn | 1338-3973 |
| language | English |
| last_indexed | 2024-12-10T21:13:55Z |
| publishDate | 2022-06-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Slovak Journal of Civil Engineering |
| spelling | doaj.art-ea014d3b1c6c4f7bae57933f5084eb862022-12-22T01:33:23ZengSciendoSlovak Journal of Civil Engineering1338-39732022-06-01302222910.2478/sjce-2022-0011A Comparison of Variational Projection and Cartographic Projection by Ritz’s MethodÁbrahámová Andrea0Vajsáblová Margita1Dept. of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology, Bratislava, SlovakiaDept. of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology, Bratislava, SlovakiaThe application of alternative mathematical methods in creating cartographic projections is an interesting factor, which affects the optimization of distortions and their distribution in the projected territory. This article presents the methodology for the creation and comparison of conformal cartographic projections formed by alternative mathematical methods of minimizing the integral criterion for scale distortion in Slovakia. The creation of the variational projection is based on the Airy-Kavraiskii criterion of evaluating the projection on the displayed area by solving Laplace's equation. The second projection is created by solving Poisson's equation using Ritz's method. Our analysis showed that the variational projection of Slovakia achieves more satisfactory distortion values than the cartographic projection created using Ritz's method. The advantage of Ritz's method is that it is possible to choose a boundary condition for a predefined undistorted convex closed curve. In this paper, we have also derived specific members of the map equations for cartographic projection based on solving Poisson's equation by Ritz's method.https://doi.org/10.2478/sjce-2022-0011cartographic projectionvariational criterionlaplace's equationpoisson's equationthe dirichlet integralritz's method |
| spellingShingle | Ábrahámová Andrea Vajsáblová Margita A Comparison of Variational Projection and Cartographic Projection by Ritz’s Method Slovak Journal of Civil Engineering cartographic projection variational criterion laplace's equation poisson's equation the dirichlet integral ritz's method |
| title | A Comparison of Variational Projection and Cartographic Projection by Ritz’s Method |
| title_full | A Comparison of Variational Projection and Cartographic Projection by Ritz’s Method |
| title_fullStr | A Comparison of Variational Projection and Cartographic Projection by Ritz’s Method |
| title_full_unstemmed | A Comparison of Variational Projection and Cartographic Projection by Ritz’s Method |
| title_short | A Comparison of Variational Projection and Cartographic Projection by Ritz’s Method |
| title_sort | comparison of variational projection and cartographic projection by ritz s method |
| topic | cartographic projection variational criterion laplace's equation poisson's equation the dirichlet integral ritz's method |
| url | https://doi.org/10.2478/sjce-2022-0011 |
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