A Computational Complexity Adaptive Nurbs Curve Interpolation Method

Abstract

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. By analyzing the calculation structure of the de Boor-Cox method when calculating the interpolation point, the calculation complexity formula for solving the interpolation point is established; the calculation structure when calculating the interpolation point by the basis function method is simplified, and the calculation complexity is reduced by sharing intermediate results, and Establish the calculation complexity formula of the basis function method solution process; establish the performance judgment formula when the de Boor-Cox method and the basis function method calculate the interpolation point, and when the curve is interpolated, dynamically select the low calculation complexity by the performance judgment formula method for interpolation. The application of the method of the invention can effectively share the intermediate results in the calculation process of the basis function algorithm, reduce the calculation complexity of the algorithm, can dynamically and adaptively select an efficient interpolation algorithm, and improve the interpolation efficiency of the NURBS curve.

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

Images