Geometric Modeling of the Valencia Orange (<i>Citrus sinensis</i> L.) by Applying Bézier Curves and an Image-Based CAD Approach
The computer-aided design of fruits are used for different purposes, e.g., to determine mechanical properties by applying engineering simulations, to design postharvest equipment, and to study the natural changes related to the topology. This paper developed a methodology to model Valencia orange (&...
Main Authors: | , , , |
---|---|
Format: | Article |
Language: | English |
Published: |
MDPI AG
2020-07-01
|
Series: | Agriculture |
Subjects: | |
Online Access: | https://www.mdpi.com/2077-0472/10/8/313 |
id |
doaj-48f7836d88a1417b996f1ea253e23dbe |
---|---|
record_format |
Article |
spelling |
doaj-48f7836d88a1417b996f1ea253e23dbe2021-04-02T06:41:54ZengMDPI AGAgriculture2077-04722020-07-011031331310.3390/agriculture10080313Geometric Modeling of the Valencia Orange (<i>Citrus sinensis</i> L.) by Applying Bézier Curves and an Image-Based CAD ApproachHector A. Tinoco0Daniel R. Barco1Olga Ocampo2Jaime Buitrago-Osorio3Experimental and Computational Mechanics Laboratory, Universidad Autónoma de Manizales, Antigua Estación del Ferrocarril, Edificio fundadores C.P., Manizales 170001, ColombiaTecno-Parque nodo Manizales, Servicio Nacional de Aprendizaje -SENA, Manizales 170001, ColombiaExperimental and Computational Mechanics Laboratory, Universidad Autónoma de Manizales, Antigua Estación del Ferrocarril, Edificio fundadores C.P., Manizales 170001, ColombiaExperimental and Computational Mechanics Laboratory, Universidad Autónoma de Manizales, Antigua Estación del Ferrocarril, Edificio fundadores C.P., Manizales 170001, ColombiaThe computer-aided design of fruits are used for different purposes, e.g., to determine mechanical properties by applying engineering simulations, to design postharvest equipment, and to study the natural changes related to the topology. This paper developed a methodology to model Valencia orange (<i>Citrus sinensis</i>), applying Bézier curves and an image-based CAD approach; the orange geometry was designed for different ripening stages. In the modeling process, a 3D construction was carried out using third-order Bézier curves, adjusted to the images taken in orthogonal planes. Four control points defined each profile to compose the geometric pattern of the orange, with geometric errors lower than 3%. Two prediction models were proposed to relate the orthogonal dimensions with a factor size; this means that two dimensions out of three can be predicted. The results showed that the shape ratios kept constant in any ripening stage; however, the radius of curvature evidenced differences in the analyzed shape profiles. The methodological framework presented in the paper might be used to draw other types of citrus fruits. This contribution is a tool to model fruits in 3D, instead of using expensive technological equipment, since it is only necessary to apply computer design tools.https://www.mdpi.com/2077-0472/10/8/313CAD-based geometric modelValencia orangegeometric model parametrizationfruit modeling3D fruitsBézier curves |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Hector A. Tinoco Daniel R. Barco Olga Ocampo Jaime Buitrago-Osorio |
spellingShingle |
Hector A. Tinoco Daniel R. Barco Olga Ocampo Jaime Buitrago-Osorio Geometric Modeling of the Valencia Orange (<i>Citrus sinensis</i> L.) by Applying Bézier Curves and an Image-Based CAD Approach Agriculture CAD-based geometric model Valencia orange geometric model parametrization fruit modeling 3D fruits Bézier curves |
author_facet |
Hector A. Tinoco Daniel R. Barco Olga Ocampo Jaime Buitrago-Osorio |
author_sort |
Hector A. Tinoco |
title |
Geometric Modeling of the Valencia Orange (<i>Citrus sinensis</i> L.) by Applying Bézier Curves and an Image-Based CAD Approach |
title_short |
Geometric Modeling of the Valencia Orange (<i>Citrus sinensis</i> L.) by Applying Bézier Curves and an Image-Based CAD Approach |
title_full |
Geometric Modeling of the Valencia Orange (<i>Citrus sinensis</i> L.) by Applying Bézier Curves and an Image-Based CAD Approach |
title_fullStr |
Geometric Modeling of the Valencia Orange (<i>Citrus sinensis</i> L.) by Applying Bézier Curves and an Image-Based CAD Approach |
title_full_unstemmed |
Geometric Modeling of the Valencia Orange (<i>Citrus sinensis</i> L.) by Applying Bézier Curves and an Image-Based CAD Approach |
title_sort |
geometric modeling of the valencia orange (<i>citrus sinensis</i> l.) by applying bézier curves and an image-based cad approach |
publisher |
MDPI AG |
series |
Agriculture |
issn |
2077-0472 |
publishDate |
2020-07-01 |
description |
The computer-aided design of fruits are used for different purposes, e.g., to determine mechanical properties by applying engineering simulations, to design postharvest equipment, and to study the natural changes related to the topology. This paper developed a methodology to model Valencia orange (<i>Citrus sinensis</i>), applying Bézier curves and an image-based CAD approach; the orange geometry was designed for different ripening stages. In the modeling process, a 3D construction was carried out using third-order Bézier curves, adjusted to the images taken in orthogonal planes. Four control points defined each profile to compose the geometric pattern of the orange, with geometric errors lower than 3%. Two prediction models were proposed to relate the orthogonal dimensions with a factor size; this means that two dimensions out of three can be predicted. The results showed that the shape ratios kept constant in any ripening stage; however, the radius of curvature evidenced differences in the analyzed shape profiles. The methodological framework presented in the paper might be used to draw other types of citrus fruits. This contribution is a tool to model fruits in 3D, instead of using expensive technological equipment, since it is only necessary to apply computer design tools. |
topic |
CAD-based geometric model Valencia orange geometric model parametrization fruit modeling 3D fruits Bézier curves |
url |
https://www.mdpi.com/2077-0472/10/8/313 |
work_keys_str_mv |
AT hectoratinoco geometricmodelingofthevalenciaorangeicitrussinensisilbyapplyingbeziercurvesandanimagebasedcadapproach AT danielrbarco geometricmodelingofthevalenciaorangeicitrussinensisilbyapplyingbeziercurvesandanimagebasedcadapproach AT olgaocampo geometricmodelingofthevalenciaorangeicitrussinensisilbyapplyingbeziercurvesandanimagebasedcadapproach AT jaimebuitragoosorio geometricmodelingofthevalenciaorangeicitrussinensisilbyapplyingbeziercurvesandanimagebasedcadapproach |
_version_ |
1724171850983931904 |