Geometric Modeling of the Valencia Orange ( Citrus sinensis 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 ( Citrus sinensis ), 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.