Constrained fitting -: A key issue in reverse engineering conventional parts

Constrained fitting is the process of approximating segmented point sets simultaneously by multiple surfaces while certain geometric constraints, such as tangency, perpendicularity, parallelism, concentricity are satisfied. This technique is particularly important in the context of reverse engineering, where geometrically and topologically consistent, near to perfect CAD models must be created. In this paper various representational and numerical problems are discussed in order to make constrained fitting computationally efficient even for large, multiple point clouds. Special emphasis is taken to resolve contradicting constraints. Simple examples of handling smooth profile curves and tangentially connected face sets are also presented.