A linear-time algorithm for computing the Voronoi diagram of a convex polygon
Discrete & Computational Geometry
Approximation algorithms for the geometric covering salesman problem
Discrete Applied Mathematics
IEEE Transactions on Pattern Analysis and Machine Intelligence
Measuring shape: ellipticity, rectangularity, and triangularity
Machine Vision and Applications
Coverage path planning algorithms for agricultural field machines
Journal of Field Robotics
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The shape and size of field plots vary in different regions of the world. In open plains, the field plots tend to be rectangular, but in other types of terrain the field plots are bounded by nature, causing them to have many types of shapes. Especially in Finland, large rectangular field plots are rare. This article presents eight indices for measuring the shapes of field plots. The indices are as follows: convexity, compactness, triangularity, rectangularity, ellipticity, the ratio of principal moments, the radius of the incircle and 'curb index'. Whereas most of the shapes are well known in computational geometry, the 'curb index' is defined in more detail in this article. The data set used for the analysis is from southern Finland and consists of approximately 65,000 field plots. The field shape indices can be used for many purposes, for instance to estimate operational efficiency, to trade farm land, to justify merging two field plots or to facilitate land consolidation projects. In this article, the shape indices are used for two purposes: to classify the real field plots and to study their relation to operational efficiency. In this article, operational efficiency is related to overhead time and distance spent in headlands. Operational efficiency is studied by comparing the shape indices with the efficiency factor, whereas a complex coverage path planning algorithm is used to obtain the overhead for the travel distance. The article presents a formula for estimating operational efficiency using shape indices, based on multivariate regression. While the shape indices measure what they are supposed to measure, the data set (from Finland) shows that only 25% of the field plots can be classified as simple shapes. However, by using a multivariate regression, a correlation was found between the shape indices and operational efficiency.