An SQP method for Chebyshev and hole-pattern fitting with geometrical elements

摘要

A customized sequential quadratic program (SQP) method for the solution of minimax-type fitting applications in coordinate metrology is presented. This area increasingly requires highly efficient and accurate algorithms, as modern three-dimensional geometry measurement systems provide large and computationally intensive data sets for fitting calculations. In order to meet these aspects, approaches for an optimization and parallelization of the SQP method are provided. The implementation is verified with medium (500 thousand points) and large (up to 13 million points) test data sets. A relative accuracy of the results in the range of 1??×??10?14 is observed. With four-CPU parallelization, the associated calculation time has been less than 5?s.