Calculation method of free-form surface intersection line

Abstract

The invention relates to a calculation method of a free-form surface intersection line. The method comprises the following steps: respectively determining a first type value point and a second type value point corresponding to a first curved surface and a second curved surface; establishing an intersection point initial value objective function according to the first type value point and the second type value point; calculating an initial value objective function by adopting a Newton-Raphson method to obtain an initial intersection point and an intersection point initial parameter; calculating a first-order differential and a second-order differential of the intersection point initial parameter on the corresponding first curved surface and the second curved surface; respectively determining respective second-order Taylor expansion; according to a second-order Taylor expansion, approximate parameters of the tracking direction and the second intersection point are determined, and an objective function of the distance between the two approximate points is established; calculating an objective function by adopting a Newton-Raphson method, and determining a second intersection point; and according to the second intersection point and the tracking direction, determining the next intersection point until the end point. The calculation method of the free curved surface intersection line aims to solve the problem that a curved surface intersection algorithm cannot meet high precision and high efficiency at the same time.

Description

technical field [0001] The invention relates to the technical field of computer-aided design, in particular to a method for calculating the intersection of free-form surfaces. Background technique [0002] Surface intersection is widely used in geometric modeling, NC machining tool path generation and so on. At present, the algorithm of surface intersection mainly adopts segmentation method and tracking method. The segmentation algorithm is to recursively segment each surface block that composes two free-form surfaces into planes until the accuracy requirement is met. This method is simple to implement, but cannot balance computational accuracy and computational efficiency. The tracking method is to first find a point on the intersection line as the initial point, calculate the approximate position of the adjacent intersection points, and repeat the tracking in turn until the boundary of the surface is reached. This method has high calculation accuracy, but is greatly aff...

AI Technical Summary

Problems solved by technology

[0005] The embodiment of the present invention provides a method for calculating the intersection line of free-form surfaces, which solves the technical problem that the surface intersection algorithm cannot simultaneously satisfy high precision and high efficiency

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