Estimation of minimum volume of bounding box for geometrical metrology

Abstract

This paper presents algorithms for estimating the minimum volume bounding box based on a three-dimensional point set measured by a coordinate measuring machine. A new algorithm, which calculates the minimum volume with high accuracy and reduced number of computations, is developed. The algorithm is based on the convex hull operation and established theories about a minimum bounding box circumscribing a convex polyhedron. The new algorithm includes a pre-processing operation that removes convex polyhedron faces located near the edges of the measured object. As showed in the paper, the solution of the minimum bonding box is not based on faces located near the edges; therefore, we can save computation time by excluding them from the convex polyhedron data set. The algorithms have been demonstrated on physical objects measured by a coordinate measuring machine, and on theoretical 3D models. The results show that the algorithm can be used when high accuracy is required, for example in calibration of reference standards.