Inspection planning and verification procedures are central activities in any inspection using Coordinates Measuring Machines (CMMs). The objective of tactile CMM inspection planning is to establish the best sequence of inspection steps with a detailed inspection procedure for each inspection feature or cluster of measurement points. Algorithms are then used to interpolate these points and generate their mathematical model(s). Complex surfaces may need to be decomposed into several patches which are interpolated separately then joined in a single model by determining their intersections. These models (curves and surfaces) are then used by tolerance analysis algorithms to verify if tolerance specifications are met by comparing the interpolated model representing the actual surface and the CAD model representing the theoretical surface.