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| Format: | Recurso digital |
| Language: | English |
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Zenodo
2025
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| Online Access: | https://doi.org/10.5281/zenodo.15183221 |
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| _version_ | 1866901771961499648 |
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| author | Gilić, Frane Gašparović, Mateo |
| author_facet | Gilić, Frane Gašparović, Mateo |
| contents | <p>To define the rHEALPix DGGS on the ellipsoids of revolution, authalic latitude (i.e., area-preserving latitude) is used to map the sphere to the ellipsoid. In the <a href="https://github.com/manaakiwhenua/rhealpixdggs-py" target="_blank" rel="noopener">rHEALPix DGGS Python codebase</a>, current statements for converting geodetic to authalic latitude and vice versa were modified in line with the research by <a href="https://doi.org/10.48550/arXiv.2212.05818">Charles F. F. Karney</a>. Modified statements are based on power-series approximation in terms of the third flattening of the ellipsoid of revolution <em>n</em>, up to <em>n</em>^6. These statements have lower truncation and round-off errors than current statements when performing double-precision floating-point calculations.</p> <p>The folder 'modifications' contains all files that have been changed in the <a href="https://github.com/manaakiwhenua/rhealpixdggs-py">rHEALPix DGGS Python codebase</a>, including the TXT file with all differences between the merge git commit (<a href="https://github.com/manaakiwhenua/rhealpixdggs-py/commit/6b669ea5a044b3bf0885b37e5beb1012ef451537">6b669ea5</a>) and the commit in the default branch before merging (<a href="https://github.com/manaakiwhenua/rhealpixdggs-py/commit/d15f30a9f2ac0aef2ab5910e772f9d9ea383807f">d15f30a</a>).</p> <p>The folder 'assessment' contains three subfolders: 'accuracy_assessment', 'execution_time_assessment', and 'cell_area_assessment'.</p> <ul> <li>The folder 'accuracy_assessment' contains a Python module for calculating errors produced by current and modified Python statements when converting authalic to geodetic latitude and vice versa, calculated errors in a CSV file, and their analysis in the XLSX file and Jupyter Notebook. It also contains the subfolder 'visualization' with Python module for generating maps showing the distribution of calculated errors, as well as GeoJSON files required for visualization and generated maps in SVG files.</li> <li>The folder 'execution_time_assessment' contains Python modules for measuring the execution time of current and modified Python statements for converting authalic to geodetic latitude and vice versa. It also contains an XLSX file with analysis of the measured execution times.</li> <li>The folder 'cell_area_assessment' contains two Python modules for calculating deviations between calculated areas of cells and their theoretical areas. One Python module should be executed in a library in which the function for converting geodetic to authalic latitude and vice versa is unaltered, and another in a library where changes/optimizations are present. Calculations are performed for 1-to-4 and 1-to-9 refinements across all resolutions (up to resolution 27 for 1-to-4 refinement and up to resolution 17 for 1-to-9 refinement). Area deviations are calculated for nine DGGS cells in each resolution (three quad, three skew quad, and three dart cells), which means that results are not comprehensive but are aimed at getting an impression of how errors in conversion between authalic and geodetic latitudes affect cell areas. This folder also contains results (CSV and GeoJSON files, as well as a summary XLSX file).</li> </ul> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_15183221 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Enhancing Authalic Latitude Calculation for the rHEALPix DGGS (supplementary material) Gilić, Frane Gašparović, Mateo accuracy authalic latitude discrete global grid system (DGGS) ellipsoids rHEALPix numerical stability <p>To define the rHEALPix DGGS on the ellipsoids of revolution, authalic latitude (i.e., area-preserving latitude) is used to map the sphere to the ellipsoid. In the <a href="https://github.com/manaakiwhenua/rhealpixdggs-py" target="_blank" rel="noopener">rHEALPix DGGS Python codebase</a>, current statements for converting geodetic to authalic latitude and vice versa were modified in line with the research by <a href="https://doi.org/10.48550/arXiv.2212.05818">Charles F. F. Karney</a>. Modified statements are based on power-series approximation in terms of the third flattening of the ellipsoid of revolution <em>n</em>, up to <em>n</em>^6. These statements have lower truncation and round-off errors than current statements when performing double-precision floating-point calculations.</p> <p>The folder 'modifications' contains all files that have been changed in the <a href="https://github.com/manaakiwhenua/rhealpixdggs-py">rHEALPix DGGS Python codebase</a>, including the TXT file with all differences between the merge git commit (<a href="https://github.com/manaakiwhenua/rhealpixdggs-py/commit/6b669ea5a044b3bf0885b37e5beb1012ef451537">6b669ea5</a>) and the commit in the default branch before merging (<a href="https://github.com/manaakiwhenua/rhealpixdggs-py/commit/d15f30a9f2ac0aef2ab5910e772f9d9ea383807f">d15f30a</a>).</p> <p>The folder 'assessment' contains three subfolders: 'accuracy_assessment', 'execution_time_assessment', and 'cell_area_assessment'.</p> <ul> <li>The folder 'accuracy_assessment' contains a Python module for calculating errors produced by current and modified Python statements when converting authalic to geodetic latitude and vice versa, calculated errors in a CSV file, and their analysis in the XLSX file and Jupyter Notebook. It also contains the subfolder 'visualization' with Python module for generating maps showing the distribution of calculated errors, as well as GeoJSON files required for visualization and generated maps in SVG files.</li> <li>The folder 'execution_time_assessment' contains Python modules for measuring the execution time of current and modified Python statements for converting authalic to geodetic latitude and vice versa. It also contains an XLSX file with analysis of the measured execution times.</li> <li>The folder 'cell_area_assessment' contains two Python modules for calculating deviations between calculated areas of cells and their theoretical areas. One Python module should be executed in a library in which the function for converting geodetic to authalic latitude and vice versa is unaltered, and another in a library where changes/optimizations are present. Calculations are performed for 1-to-4 and 1-to-9 refinements across all resolutions (up to resolution 27 for 1-to-4 refinement and up to resolution 17 for 1-to-9 refinement). Area deviations are calculated for nine DGGS cells in each resolution (three quad, three skew quad, and three dart cells), which means that results are not comprehensive but are aimed at getting an impression of how errors in conversion between authalic and geodetic latitudes affect cell areas. This folder also contains results (CSV and GeoJSON files, as well as a summary XLSX file).</li> </ul> |
| title | Enhancing Authalic Latitude Calculation for the rHEALPix DGGS (supplementary material) |
| topic | accuracy authalic latitude discrete global grid system (DGGS) ellipsoids rHEALPix numerical stability |
| url | https://doi.org/10.5281/zenodo.15183221 |