本文選題：支撐函數(shù) + 剖分�。� 參考：《中國石油大學(xué)(北京)》2016年碩士論文

【摘要】：近年來,隨著科學(xué)技術(shù)的迅猛發(fā)展,來自各種科學(xué)計算、工程計算、測量等方面的數(shù)據(jù)日益增大,所要求的精度日益精確,待處理的問題規(guī)模越來越大,因而,研究大規(guī)模散亂數(shù)據(jù)的曲面重構(gòu)日益成為迫切要解決的問題。本文對基于大規(guī)模的散亂數(shù)據(jù)的曲面重構(gòu)問題進(jìn)行了研究。首先,構(gòu)造了一個擬合函數(shù)進(jìn)行隱式曲面的重構(gòu)。其次,通過采用積分構(gòu)造樣條函數(shù)方法和樣條函數(shù)空間的Ⅲ-型剖分,構(gòu)造出了Box樣條的分段多項式形式作為擬合函數(shù)的基函數(shù)。然后,通過運用最小二乘法的思想,將Box樣條函數(shù)引入到曲面重構(gòu)中,求解出擬合函數(shù)的控制系數(shù)。最后,根據(jù)擬合函數(shù)進(jìn)行曲面重構(gòu),同時進(jìn)行分析討論了該算法計算效率和時間復(fù)雜度,并通過實例分析驗證了算法的效率和擬合結(jié)果。具體研究工作如下:(1)完成對Box樣條的構(gòu)造�；冖�-型剖分對樣條函數(shù)空間進(jìn)行處理,通過積分方法求得樣條函數(shù)的局部支集。(2)通過構(gòu)造的非張量積代數(shù)Box樣條函數(shù),對隱函數(shù)進(jìn)行重構(gòu)。在張量積代數(shù)B-樣條曲面重構(gòu)算法的基礎(chǔ)上,將三個一維B樣條相乘,轉(zhuǎn)換成一個Box樣條基函數(shù),大大減少了運算量;而且,將三個一維B樣條無法擬合的點,在相同的階次上進(jìn)行了擬合。
[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，

本文編號：1892573