Free-form surface localization using surface partitioning and genetic algorithm

Free-form surfaces are usually described using the relationships of parametric surfaces such as Bezier, B-Spline and NURBS. The computer-aided design systems use NURBS to describe complex (complicated) geometries. Free-form surfaces known as complex (complicated) surfaces are widely used in a variety of industries such as ship-building and molding, inspection of these surfaces is therefore of high importance (very important). Considering that measured free-form surfaces and design models are located in two different coordinate systems, finding the similarity of free-form surfaces and placing them in an identical coordinates system is necessary to compare these surfaces, this process is called localization. This paper introduces a feature and curvature based method for the automatic localization and comparison of free-form surfaces for inspection with coordinate measuring machine (CMM). This method localizes the measurement surface to the design model through two steps. The first step is general localization which is accomplished based on the relation and similarity between curvatures of free-form surfaces and zoning these surfaces to concave, convex and saddle areas. The second step is fine localization based on genetic algorithm which considers correspondence in the form of point to point. The simulation results show that the localization accuracy of the proposed method for the 50 × 50 mm aluminum workpiece of was about 0.02 mm, which is 56 percent less than the value obtained from the iterative closest point method.