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Numerical Modeling of the Shape of Agricultural Products on the Example of Cucumber Fruits

Department of Heavy Duty Machines and Research Methodology, University of Warmia and Mazury in Olsztyn, Olsztyn 10-957, Poland
Author to whom correspondence should be addressed.
Sustainability 2019, 11(10), 2798;
Received: 24 April 2019 / Revised: 11 May 2019 / Accepted: 14 May 2019 / Published: 16 May 2019
(This article belongs to the Special Issue Sustainable Production in Food and Agriculture Engineering)
PDF [3316 KB, uploaded 16 May 2019]


The aim of the study was to build numerical models of cucumbers cv. Śremski with the use of a 3D scanner and to analyze selected geometric parameters of cucumber fruits based on the developed models. The basic dimensions of cucumber fruits–length, width and thickness—were measured with an electronic caliper with an accuracy of d = 0.01 mm, and the surface area and volume of fruits were determined by 3D scanning. Cucumber fruits were scanned with an accuracy of d = 0.13 mm. Six models approximating the shape of cucumber fruits were developed with the use of six geometric figures and their combinations to calculate the surface area and volume of the analyzed agricultural products were identified. The surface area and volume of cucumber fruits calculated by 3D scanning and mathematical formulas were compared. The surface area calculated with the model combining two truncated cones and two hemispheres with different diameters, joined base-to-base, was characterized by the smallest relative error of 3%. Fruit volume should be determined with the use of mathematical formulas derived for a model composed of an ellipsoid and a spheroid. The proposed geometric models can be used in research and design. View Full-Text
Keywords: 3D scanner; geometric model; reverse engineering; fruit; cucumber 3D scanner; geometric model; reverse engineering; fruit; cucumber

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Anders, A.; Choszcz, D.; Markowski, P.; Lipiński, A.J.; Kaliniewicz, Z.; Ślesicka, E. Numerical Modeling of the Shape of Agricultural Products on the Example of Cucumber Fruits. Sustainability 2019, 11, 2798.

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