A Contribution to Recognize Shape and Position of Basic Functional Geometries Obtained by Mechanical Manufacturing

The main objective of this study was to establish an algorithm capable to recognize the shape and position of basic functional geometries obtained by mechanical manufacturing. Differential geometry was used to determine Gaussian and mean local curvatures of surfaces described by ordered cloud point representation. The partial derivatives were taken the entire sets of data points and the Gaussian and mean curvatures were then obtained, enabling geometrical shape identification and position. Since the initial data was a set of discrete points, the divided difference method was used in order to determine a numerical approximation to the partial derivatives at each point. The Gaussian and mean curvatures were used to implement the proposed algorithm through a MATLAB application. It was first tested using geometrical data generated on MATLAB and then using a set of points measured from an actual physical shape, using a coordinate measuring machine. The results obtained validated the adequacy and the potential of the proposed algorithm to identify and spatially locate shapes that commonly need to be measured.