Bezier curve surface fitting method and system based on de Casteljau algorithm

Abstract

The invention discloses a bezier curve surface fitting method and system based on the de Casteljau algorithm. The method includes the steps of obtaining n data points of a Bezier curve, obtaining 2*(n-2) control points through the n data points of the Bezier curve according to the de Casteljau algorithm, setting control coefficients at the control points, and obtaining the Bezier curve by adjusting the curvature, at the data points, of the Bezier curve by changing the control coefficients, and by determining the control coefficients when the curvature is the target curvature. According to the method, fitting is conducted on the Bezier curve surface by changing the control coefficients, the Bezier curve which is high in profile modeling degree can be obtained through fitting when a small number of data points are selected according to actual application, it is ensured that the curve can pass through all the data points, continuity of the curve is ensured at the data points, and on the aspect of curve fitting, complexity is lowered, and fitting efficiency is improved.

Description

technical field [0001] The invention relates to the field of computer graphics, in particular to a Bezier curve and surface fitting method and system based on De Castrio's algorithm. Background technique [0002] A Bezier curve is a curve that passes through the start and end control points, and the shape of the curve can be adjusted through the middle control points. As the degree of the Bezier curve increases, that is, when there are multiple control points, the curve will become unstable, and local modification cannot be performed, and the flexibility is not high enough. Therefore, in the research field of computer graphics, researchers will use B-spline curves. It is a curve model based on the Bezier curve. While ensuring the advantages of the Bezier curve, its local characteristics and approximation degree will be improved compared with the Bezier curve. In terms of surface fitting, the algorithms for Bezier surfaces and B-spline surfaces are to define curves in the u...

AI Technical Summary

Problems solved by technology

[0003] However, in the process of using B-splines, it is found that this kind of curve model is more complicated to use and cannot meet the actual needs of the project. In addition, in order to pass known type value points, the existing algorithms often use when calculating the corresponding control points. The method of directly solving the linear equation system, which makes the order of the equation system increase with the increase of the number of value points, resulting in a very large amount of calculation, and the control points obtained by this algorithm are not adjustable, resulting in the fitted Bezier The curve will jump locally and cannot be limited

Images