B-spline Fitting Of The Free Surface

By now free form surface modeling is an important research branch of CAD/CAGD, it is also the foundation of CAM technology. For the numerical control machining of complex free form surface, the first task is to perform free form surface modeling. The aim of this dissertation is to perform complex free form surface modeling by choosing appropriate methods, then it can satisfy the requirements of numerical control machining.This paper introduces the basic theory of B-spline curves and surfaces, studies the fundamental geometric algorithms of B-spline curves and surfaces. It analyses the fair approximating method of B-spline curves, by introduced fair weight term and deviate weight term in the process of B-spline curves approximating, the obtained B-spline can well close to the given points. Aim at the instance that given points measured on the different section of the surface are nonuniform between sections and the numbers of measured points are not same between sections of the surface, this dissertation gives a approximating method of B-spline surface based on digitized section points, for the case that the numbers of measured points have great difference between sections, this paper addresses a approximating method of B-spline surface based on degree elevation. Raising the degree of the curve which is on the section whose measured points is less than the other sections, it can add extra control points and ensure the approximating precision of the surface. This paper has also given the calculate method of approximating precision of B-spline surface.Reliability of theory and the result of numerical examples indicate that the method in this paper is viable. It can bring a new way to complex free form surface modeling and create favorable conditions to following numerical control machining.