Parabola Error Evaluation Based on Geometry Optimizing Approximation Algorithm

ABSTRACT

A more accurate evaluation for parabola errors based on Geometry Optimizing Approximation Algorithm (GOAA) is presented in this paper. Firstly, according to the least squares method, two parabola characteristic points are determined as reference points to form a series of auxiliary points according to a certain geometry shape, and then, assumption ideal auxiliary parabolas are reversed by the parabola geometric characteristic. The range distance of all given points to the assumption ideal parabolas are calculated by the auxiliary parabolas as supposed ideal parabolas, and the reference points, the auxiliary points, reference parabola and auxiliary parabolas are reconstructed by comparing the range distances, the evaluation for parabola error is finally obtained after repeating this entire process. On the basis of 0.1 mm of a group of simulative metrical data, compared with the least square method, while the criteria of stop searching is 0.00001 mm, the parabola error value from this algorithm can be reduced by 77 μm. The result shows this algorithm realizes the evaluation of parabola with minimum zone, accurately and stably.

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