Validation of 3-D curved objects: CAD model and fabricated workpiece

This paper proposes a new method to describe and identify a 3-D curved object for the purpose of validating a fabricated object to the design specification. Curved 3-D objects are, in general, difficult to represent and identify because they lack distinct properties such as edges, planes, or cylindrical surfaces which are the building blocks in representing objects. In this paper, the authors propose to use principal axes of a 3-D object to establish a reference for the representation. A method of obtaining an inertia matrix from a 3-D range image is developed. The unique set of principal axes is obtained from the inertia matrix of an object with an arbitrary 3-D position and orientation, and the object can be described uniquely on these principal axes. On the principal axes, an object is described by a set of features describing the shape of the object such as spine, section size, section orientation, and section contraction. The features are used for comparing two objects for the validation purpose. The authors also propose a direct measure of similarity between two objects as a mean-squared difference of radii. As an experiment, two 3-D object models are designed through a CAD package, and fabricated objects are compared with the designed models for validation purposes