Computational complexity self-adaptation NURBS splined interpolation method

Abstract

The invention relates to the interpolation point computing technology of a numerical control system, in particular to a computational complexity self-adaptation NURBS splined interpolation method. By analyzing the computing structure generated when an interpolation point is computed with a de Boor-Cox method, a computational complexity formula for solving the interpolation point is built; the computing structure generated when the interpolation point is computed with a basis function method is simplified, the computational complexity is reduced by sharing an intermediate result, and a computational complexity formula used in the solving process of the basis function method is built; the performance judgment formulas generated when the interpolation point is computed with the de Boor-Cox method and the basis function method are built, and in the splined interpolation process, the method low in computational complexity is dynamically selected through the performance judgment formulas for interpolation. By the application of the method, the intermediate result in the computing process of a basis function algorithm can be effectively shared, the computational complexity of the algorithm is reduced, an efficient interpolation algorithm can be dynamically selected in a self-adaptation mode, and the NURBS splined interpolation efficiency is improved.

Description

technical field [0001] The invention relates to an interpolation point calculation technology of a numerical control system, in particular to a NURBS curve interpolation method with self-adaptive calculation complexity. Background technique [0002] In 1991, the International Organization for Standardization (ISO) used NURBS as the only representation of free-form curves and surfaces in the standard for the exchange of product model data (STEP) defined by industrial product geometry. With the establishment of the STEP-NC (ISO14649) standard, the research on the direct interpolation technology of NURBS curves and curved surfaces in the numerical control system has gradually increased. Since the NURBS curve cannot be expressed by a unified analytical formula, there is a problem of high computational complexity in the calculation of interpolation points on curves and curved surfaces, resulting in a large amount of calculation time required for the calculation of interpolation p...

AI Technical Summary

Problems solved by technology

[0003] The existing calculation methods of interpolation points are mainly divided into the following categories: one is to use iterative solution, which is easy to implement by computer, but the average calculation complexity is the highest

The second is to use the basis function method to solve the problem. During the solution process, the evaluation of each basis function only needs to be calculated once, but there are problems such as the large amount of calculation for solving the basis function and the sharing of intermediate results.

The third is to use the de-Boor Cox algorithm to solve the problem. This method avoids the calculation of the B-spline basis function and directly iteratively calculates the control points. The average calculation complexity of the interpolation point calculation is the lowest, but the performance of the algorithm varies with the parameters of the NURBS curve. Will fluctuate, with lowest performance in extreme cases

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