Solid-model generation from measured point data

The paper addresses the issue of solid-model generation from coordinate-measuring machine (CMM) point data. All the surfaces of an object are measured, with some in different orientations, and transformations are performed on the point data to convert it into a consistent coordinate system in order for correct representations for all the surfaces to be obtained. A method based on the least-squares approach is used to fit quadric surfaces to the measured point data, resulting in an algebraic representation for each surface. Using the surface equations and the topology information from an original CAD solid model, the edges and vertices are found by the direct intersection of the corresponding fitted surfaces. Thus, a complete B-rep solid-model data structure is created for the measured object from the CMM point data. Theory, algorithms and examples are presented, with discussions on uncertainty issues in measurement, fitting and topology. The algorithms developed are useful for the inspection of manufactured components and assemblies, assembly fit-up analysis, uncertainty analysis and reverse engineering.