Approximation of the soil particle-size distribution curve using a NURBS curve
Soil particle-size distribution or soil texture presents one of the most important physical properties. There are various systems of the classification systems for soil particle-size fractions with different boundaries. Our effort was concentrated on the mathematical approach to evaluate the existin...
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Czech Academy of Agricultural Sciences
2025-01-01
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| Series: | Soil and Water Research |
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| Online Access: | https://swr.agriculturejournals.cz/artkey/swr-202501-0002_approximation-of-the-soil-particle-size-distribution-curve-using-a-nurbs-curve.php |
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| author | Adéla Marie Marhoul Tomáš Herza Josef Kozák Jaroslava Janků Jan Jehlička Luboš Borůvka Karel Němeček Miroslav Jetmar Petr Polák |
| author_facet | Adéla Marie Marhoul Tomáš Herza Josef Kozák Jaroslava Janků Jan Jehlička Luboš Borůvka Karel Němeček Miroslav Jetmar Petr Polák |
| author_sort | Adéla Marie Marhoul |
| collection | DOAJ |
| description | Soil particle-size distribution or soil texture presents one of the most important physical properties. There are various systems of the classification systems for soil particle-size fractions with different boundaries. Our effort was concentrated on the mathematical approach to evaluate the existing data and convert it to the form of a reconstructed cumulative particle-size curve which will allow reading concentration of any desired particle size. Non-Uniform Rational B-Splines (NURBS) curves therefore represent a generalization of B-splines and Bézier curves by extending the definition by an element of rationality, which is represented by the weights of the control points, and a nodal vector of parametrization, which represents the element of uniformity. The NURBS curve was used for smooth (depending on the degree of the curve used) and as tight as possible approximation of the arranged control points, the connecting lines of which forms a convex envelope for its individual parts. The NURBS approximation curve is therefore determined by the ordered control points and their connecting lines, the weights of these points, the degree of the curve and the nodal vector of parametrization. However, the construction of the approximation curve is primarily dependent on a limited number of points of the experimentally determined particle-size distribution curves, and for curves with significant breaks in the course, one must consider either a lower accuracy of the approximation or the necessity of "improving" the approximation using the weights of individual points, inserting additional points or working with a nodal vector of parametrization. For basic approximation, the PUGIS system (Czech soil information system) offers automatic approximation using all variants mentioned in the article as well as the possibility of individual changes in the weights of control points, in their number and position, and in the nodal vector of parametrization. |
| format | Article |
| id | doaj-art-daf19d60387e4a50985401e76475a08f |
| institution | Kabale University |
| issn | 1801-5395 1805-9384 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Czech Academy of Agricultural Sciences |
| record_format | Article |
| series | Soil and Water Research |
| spelling | doaj-art-daf19d60387e4a50985401e76475a08f2025-01-14T12:45:14ZengCzech Academy of Agricultural SciencesSoil and Water Research1801-53951805-93842025-01-01201163110.17221/139/2024-SWRswr-202501-0002Approximation of the soil particle-size distribution curve using a NURBS curveAdéla Marie Marhoul0Tomáš Herza1Josef Kozák2Jaroslava Janků3Jan Jehlička4Luboš Borůvka5Karel Němeček6Miroslav Jetmar7Petr Polák8Department of Soil Science and Soil Protection, Faculty of Agrobiology, Food and Natural Resources, Czech University of Life Sciences Prague, Prague, Czech RepublicHydrosoft Veleslavín s.r.o., Prague, Czech RepublicDepartment of Soil Science and Soil Protection, Faculty of Agrobiology, Food and Natural Resources, Czech University of Life Sciences Prague, Prague, Czech RepublicDepartment of Soil Science and Soil Protection, Faculty of Agrobiology, Food and Natural Resources, Czech University of Life Sciences Prague, Prague, Czech RepublicDepartment of Environmental Geosciences, Faculty of the Environmental Sciences, Czech University of Life Sciences Prague, Prague, Czech RepublicDepartment of Soil Science and Soil Protection, Faculty of Agrobiology, Food and Natural Resources, Czech University of Life Sciences Prague, Prague, Czech RepublicDepartment of Soil Science and Soil Protection, Faculty of Agrobiology, Food and Natural Resources, Czech University of Life Sciences Prague, Prague, Czech RepublicDepartment of Environmental Geosciences, Faculty of the Environmental Sciences, Czech University of Life Sciences Prague, Prague, Czech RepublicDepartment of Soil Science and Soil Protection, Faculty of Agrobiology, Food and Natural Resources, Czech University of Life Sciences Prague, Prague, Czech RepublicSoil particle-size distribution or soil texture presents one of the most important physical properties. There are various systems of the classification systems for soil particle-size fractions with different boundaries. Our effort was concentrated on the mathematical approach to evaluate the existing data and convert it to the form of a reconstructed cumulative particle-size curve which will allow reading concentration of any desired particle size. Non-Uniform Rational B-Splines (NURBS) curves therefore represent a generalization of B-splines and Bézier curves by extending the definition by an element of rationality, which is represented by the weights of the control points, and a nodal vector of parametrization, which represents the element of uniformity. The NURBS curve was used for smooth (depending on the degree of the curve used) and as tight as possible approximation of the arranged control points, the connecting lines of which forms a convex envelope for its individual parts. The NURBS approximation curve is therefore determined by the ordered control points and their connecting lines, the weights of these points, the degree of the curve and the nodal vector of parametrization. However, the construction of the approximation curve is primarily dependent on a limited number of points of the experimentally determined particle-size distribution curves, and for curves with significant breaks in the course, one must consider either a lower accuracy of the approximation or the necessity of "improving" the approximation using the weights of individual points, inserting additional points or working with a nodal vector of parametrization. For basic approximation, the PUGIS system (Czech soil information system) offers automatic approximation using all variants mentioned in the article as well as the possibility of individual changes in the weights of control points, in their number and position, and in the nodal vector of parametrization.https://swr.agriculturejournals.cz/artkey/swr-202501-0002_approximation-of-the-soil-particle-size-distribution-curve-using-a-nurbs-curve.phpdata harmonizationlegacy soil databasemathematical approachsoil particles cumulative curve restorationsoil texture |
| spellingShingle | Adéla Marie Marhoul Tomáš Herza Josef Kozák Jaroslava Janků Jan Jehlička Luboš Borůvka Karel Němeček Miroslav Jetmar Petr Polák Approximation of the soil particle-size distribution curve using a NURBS curve Soil and Water Research data harmonization legacy soil database mathematical approach soil particles cumulative curve restoration soil texture |
| title | Approximation of the soil particle-size distribution curve using a NURBS curve |
| title_full | Approximation of the soil particle-size distribution curve using a NURBS curve |
| title_fullStr | Approximation of the soil particle-size distribution curve using a NURBS curve |
| title_full_unstemmed | Approximation of the soil particle-size distribution curve using a NURBS curve |
| title_short | Approximation of the soil particle-size distribution curve using a NURBS curve |
| title_sort | approximation of the soil particle size distribution curve using a nurbs curve |
| topic | data harmonization legacy soil database mathematical approach soil particles cumulative curve restoration soil texture |
| url | https://swr.agriculturejournals.cz/artkey/swr-202501-0002_approximation-of-the-soil-particle-size-distribution-curve-using-a-nurbs-curve.php |
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