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2 ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes

2 2017

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A mathematical method for modeling the shape of apples. Part 2. Calculation and validation of results

Mieszkalski L., Wojdalski J.

ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes

2017

Vol. 6, No 3

105--109

The aim of the study was to propose a mathematical method for modeling the shape of apples cv. Ligol and their anatomical parts, the locule and the pericarp, with the use of Bézier curves. The method developed in part 1 of the study was used to generate 3D models describing the shape of an apple, the locule and the pericarp. The main projection planes of the apple, locule and pericarp were compared with their corresponding models to reveal that the proposed method supports modeling of geometric solids with sufficient accuracy for practical applications.

A mathematical method for modeling the shape of apples. Part 1. Description of the method

Mieszkalski L., Wojdalski J.

ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes

2017

Vol. 6, No 3

97--104

This study proposes a mathematical method for modeling the shape of apples, locules and pericarps with the use of Bézier curves. The concave and convex parts of apples cv. Ligol were described with three smoothly-joined Bézier curves. Contours were described based on images of an apple rotated at intervals of 36° relative to its natural axis of symmetry. A 3D model was formed by Bézier curves positioned along the apple’s meridians. The shape of the locule and the pericarp was described with the use of two smoothly-joined Bézier curves each, rotated relative to the apple’s longitudinal axis.