Soil & Water Res., 2025, 20(1):16-31 | DOI: 10.17221/139/2024-SWR
Approximation of the soil particle-size distribution curve using a NURBS curveOriginal Paper
- Adéla Marie Marhoul1, Tomáš Herza2, Josef Kozák1*, Jaroslava Janků
ORCID...1, Jan Jehlička3, Luboš Borůvka1, Karel Němeček1, Miroslav Jetmar3, Petr Polák1,4 - 1 Department of Soil Science and Soil Protection, Faculty of Agrobiology, Food and Natural Resources, Czech University of Life Sciences Prague, Prague, Czech Republic
- 2 Hydrosoft Veleslavín s.r.o., Prague, Czech Republic
- 3 Department of Environmental Geosciences, Faculty of the Environmental Sciences, Czech University of Life Sciences Prague, Prague, Czech Republic
- 4 Ministry of Finance of the Czech Republic, Prague, Czech Republic
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.
Keywords: data harmonization; legacy soil database; mathematical approach; soil particles cumulative curve restoration; soil texture
Received: November 11, 2024; Revised: November 18, 2024; Accepted: November 19, 2024; Prepublished online: January 3, 2025; Published: January 13, 2025 Show citation
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