Three-Dimensional Geometric Modeling of Processing Tomatoes

Abstract

Characterizing tomato geometries would facilitate computer-based engineering simulation for processing optimization and equipment design. This research sought to develop a three-dimensional geometric model that can represent the morphological attributes of processing tomatoes of different masses and heights. A new tomato shape equation was derived as a function of radius in a polar coordinate system and includes the dimensional parameters and shape coefficients. To determine the unknown coefficients in the shape equation, an analytical relationship between tomato shape and size was deduced and then correlated to the distribution of tomato mass and height through linear regression analysis. A finite element meshing method was used to generate geometric models in three- and two-dimensional forms for describing the variability of size and shape. Validations of the three-dimensional model with experimentally measured values of tomato mass and surface area resulted in good precision and accuracy in terms of R2, RMSE, and RPE values. It is concluded that the developed equation and model are useful for quantifying a number of tomato geometric attributes, such as volume, surface area, radius of curvature, etc. Because the equation captures the important shape features of tomatoes with simple measurements, it is a practical and effective tool for many applications related to tomato processing and handling.