The geometric characterization of mouldboard plough surfaces by using splines

For historic reasons, mouldboard ploughs have a wide variety of surfaces. The concentration of manufacturers has reduced the number of different types but there are still few complete geometric descriptions of the surfaces of a mouldboard plough. With the aim of describing and characterizing the three-dimensional shape of the plough, permitting the obtaining of a tool for an adequate preparation of the soil for cultivation, as well as reducing labour costs, in this work different approximation methods of three-dimensional surfaces have been explored. The results obtained allow us to conclude that the application of non uniform rational B-splines, combined with an optimization algorithm based on assigning different weights to the control points of the surface analyzed, is a method which succeeds in improving the quality of the fit with respect to other algorithms proposed by several authors in different previous works also based on the use of splines. ot mean square error of the fit of these algorithms to a mouldboard plough was the lowest 1.9 mm in the observed, and increases up to 14.4 mm using a simple Bézier bicubic parametric surface. Using the efficiency index of Nash and Sutclife (1970), the highest value, 0.995, corresponded to the non uniform rational B-splines method.