Simplification of 2D shapes with equivalent rectangles
Real objects in horizontal projection often have a complex geometry. Their irregular shape causes issues during analyses and calculations that consider their geometry. The paper proposes the replacement of real-world objects with equivalent rectangles (ER). The paper also defines the geometric crite...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Polish Academy of Sciences
2022-05-01
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| Series: | Advances in Geodesy and Geoinformation |
| Subjects: | |
| Online Access: | https://journals.pan.pl/Content/123255/PDF/e14.pdf |
| _version_ | 1797690577025761280 |
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| author | Andrzej Kwinta Joanna Bac-Bronowicz |
| author_facet | Andrzej Kwinta Joanna Bac-Bronowicz |
| author_sort | Andrzej Kwinta |
| collection | DOAJ |
| description | Real objects in horizontal projection often have a complex geometry. Their irregular shape causes issues during analyses and calculations that consider their geometry. The paper proposes the replacement of real-world objects with equivalent rectangles (ER). The paper also defines the geometric criteria of ER as well as ER parameters and methods for calculating them. The paper also demonstrates the difference in the duration of calculations for different types of rectangles (equivalent rectangle with the same area, surrounding rectangle with the smallest area, inscribed rectangle with the largest area). The presented approach has been illustrated with three case studies. The first one is the application of ER to underground mining cavities to determine post-mining deformations of the ground surface. In the second study, an ER was applied to analyse the geometry of agricultural parcels in a selected part of a rural settlement. ER can help assess whether the spatial layout is faulty and if a planning intervention is necessary. The third example describes a building’s geometry with an ER. Regarding the simplification of building’s geometry, it is crucial to replace a simplified building with a model that has the same centroid location and the same area. It is the perfect solution for rapid analyses of displaying objects on maps in various scales. |
| first_indexed | 2024-03-12T02:01:18Z |
| format | Article |
| id | doaj.art-7dfeb47eed95421097b6522fac1723f5 |
| institution | Directory Open Access Journal |
| issn | 2720-7242 |
| language | English |
| last_indexed | 2024-03-12T02:01:18Z |
| publishDate | 2022-05-01 |
| publisher | Polish Academy of Sciences |
| record_format | Article |
| series | Advances in Geodesy and Geoinformation |
| spelling | doaj.art-7dfeb47eed95421097b6522fac1723f52023-09-07T13:08:17ZengPolish Academy of SciencesAdvances in Geodesy and Geoinformation2720-72422022-05-01vol. 71No 1https://doi.org/10.24425/gac.2022.141167Simplification of 2D shapes with equivalent rectanglesAndrzej Kwinta0https://orcid.org/0000-0002-2003-7703Joanna Bac-Bronowicz1https://orcid.org/0000-0001-9038-1131University of Agriculture in Krakow, Krakow, PolandWroclaw University of Science and Technology, Wroclaw, PolandReal objects in horizontal projection often have a complex geometry. Their irregular shape causes issues during analyses and calculations that consider their geometry. The paper proposes the replacement of real-world objects with equivalent rectangles (ER). The paper also defines the geometric criteria of ER as well as ER parameters and methods for calculating them. The paper also demonstrates the difference in the duration of calculations for different types of rectangles (equivalent rectangle with the same area, surrounding rectangle with the smallest area, inscribed rectangle with the largest area). The presented approach has been illustrated with three case studies. The first one is the application of ER to underground mining cavities to determine post-mining deformations of the ground surface. In the second study, an ER was applied to analyse the geometry of agricultural parcels in a selected part of a rural settlement. ER can help assess whether the spatial layout is faulty and if a planning intervention is necessary. The third example describes a building’s geometry with an ER. Regarding the simplification of building’s geometry, it is crucial to replace a simplified building with a model that has the same centroid location and the same area. It is the perfect solution for rapid analyses of displaying objects on maps in various scales.https://journals.pan.pl/Content/123255/PDF/e14.pdfequivalent rectanglegeometry simplificationunderground mining cavitiesagricultural parcelsbuilding geometry |
| spellingShingle | Andrzej Kwinta Joanna Bac-Bronowicz Simplification of 2D shapes with equivalent rectangles Advances in Geodesy and Geoinformation equivalent rectangle geometry simplification underground mining cavities agricultural parcels building geometry |
| title | Simplification of 2D shapes with equivalent rectangles |
| title_full | Simplification of 2D shapes with equivalent rectangles |
| title_fullStr | Simplification of 2D shapes with equivalent rectangles |
| title_full_unstemmed | Simplification of 2D shapes with equivalent rectangles |
| title_short | Simplification of 2D shapes with equivalent rectangles |
| title_sort | simplification of 2d shapes with equivalent rectangles |
| topic | equivalent rectangle geometry simplification underground mining cavities agricultural parcels building geometry |
| url | https://journals.pan.pl/Content/123255/PDF/e14.pdf |
| work_keys_str_mv | AT andrzejkwinta simplificationof2dshapeswithequivalentrectangles AT joannabacbronowicz simplificationof2dshapeswithequivalentrectangles |