非张量积代数B样条曲面的重构算法的研究

发布时间：2018-05-15 13:01

  本文选题：支撑函数 + 剖分　； 参考：《中国石油大学(北京)》2016年硕士论文

【摘要】：近年来,随着科学技术的迅猛发展,来自各种科学计算、工程计算、测量等方面的数据日益增大,所要求的精度日益精确,待处理的问题规模越来越大,因而,研究大规模散乱数据的曲面重构日益成为迫切要解决的问题。本文对基于大规模的散乱数据的曲面重构问题进行了研究。首先,构造了一个拟合函数进行隐式曲面的重构。其次,通过采用积分构造样条函数方法和样条函数空间的Ⅲ-型剖分,构造出了Box样条的分段多项式形式作为拟合函数的基函数。然后,通过运用最小二乘法的思想,将Box样条函数引入到曲面重构中,求解出拟合函数的控制系数。最后,根据拟合函数进行曲面重构,同时进行分析讨论了该算法计算效率和时间复杂度,并通过实例分析验证了算法的效率和拟合结果。具体研究工作如下:(1)完成对Box样条的构造。基于Ⅲ-型剖分对样条函数空间进行处理,通过积分方法求得样条函数的局部支集。(2)通过构造的非张量积代数Box样条函数,对隐函数进行重构。在张量积代数B-样条曲面重构算法的基础上,将三个一维B样条相乘,转换成一个Box样条基函数,大大减少了运算量;而且,将三个一维B样条无法拟合的点,在相同的阶次上进行了拟合。
[Abstract]:In recent years, with the rapid development of science and technology, the data from all kinds of scientific calculation, engineering calculation, measurement and so on are increasing, the precision required is becoming more and more accurate, and the scale of problems to be dealt with is becoming larger and larger. It is an urgent problem to study the surface reconstruction of large-scale scattered data. In this paper, the problem of surface reconstruction based on large scale scattered data is studied. Firstly, a fitting function is constructed to reconstruct the implicit surface. Secondly, the piecewise polynomial form of Box spline is constructed as the basis function of fitting function by using integral to construct spline function and the third type partition of spline function space. Then, by using the idea of least square method, the Box spline function is introduced into the surface reconstruction, and the control coefficient of the fitting function is solved. Finally, the surface reconstruction is carried out according to the fitting function, and the computational efficiency and time complexity of the algorithm are analyzed and discussed, and the efficiency and fitting results of the algorithm are verified by an example. The detailed research work is as follows: 1) the construction of Box spline is completed. This paper deals with the space of spline function based on type 鈪，

本文编号：1892573