自由曲面的B样条拟合

【作者】 游洪；

【导师】 曹利新；

【作者基本信息】 大连理工大学 ， 机械制造及其自动化， 2003， 硕士

【摘要】 自由曲面造型是当前CAD／CAGD的一个重要研究方向，也是CAM技术的基础。要对复杂自由曲面进行数控加工，首要任务是进行自由曲面的造型。本文的出发点是通过选用适合方法对复杂自由曲面进行造型，满足曲面数控加工的需要。论文介绍了B样条曲线曲面的基础理论，研究了B样条曲线曲面的基本几何计算。分析了B样条曲线的光顺逼近方法，在曲线逼近过程中通过引入光顺权与偏离权因子，使得到的B样条曲线更加贴近已知的型值点。针对工程上按截面测量数据组织曲面中各截面间的测量点既不均匀，截面间点数又不相同的情况，文中给出了面向截面数据的B样条曲面逼近方法，并对截面测量数据点数相差较大的情况，提出了基于升阶的B样条曲面逼近方法，通过对截面线上数据点个数较少的截面曲线进行升阶，增加了控制顶点数，保证了曲面最后的逼近精度。文中还给出了B样条曲面逼近精度的计算方法。理论的可靠和数值算例结果表明，论文中采用的方法是可行的。它将为复杂自由曲面的造型提供一种新的思路，为后续的数控加工创造有利条件。更多还原

【Abstract】 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.更多还原