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Verification of shape conformance for freeform curves and surfaces is commonly achieved by minimizing the sum of square deviations between measured points and a nominal curve/surface, thereby solving an optimal parameter estimation (OPE) problem. Finding the optimal rigid body transformation (ORB) between the measured points and nominal surface, an important step in the OPE problem, traditionally has involved iteratively solving a nonlinear optimization problem in six variables. In this paper we demonstrate that the optimization problem in six variables may be reduced to solving four, degree two implicit equations in four variables, which can be regarded as an eigen value problem. This results in considerable savings in the number of computations. A thorough analysis of the savings in computations and several examples are presented.

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Published: 11/01/1999 Number of Pages: 6 File Size: 1 file , 750 KB