Efficient registration of NURBS geometry

Abstract

The paper presents an implementation of free-form surface registration in relation to inspection of engineering components, defined as NURBS. Registration is principally performed through the Iterative Closest Point (ICP) method. The time-critical step in ICP was found to be the determination of the closest points on NURBS to a given point in space. Significant speed improvements were achieved through the adoption of a dual surface representation, involving approximation of NURBS entities by a polyhedral mesh. A criterion for sufficient polyhedral approximation was derived and implemented, producing encouraging results. Original solutions are suggested in order to further improve the computational speed. Extensive testing has been carried out, showing that the proposed registration method handles a full six degrees of freedom and achieves global convergence. Performance of the implemented algorithms is discussed with reference to registration of a turbine blade airfoil.