發(fā)布時(shí)間：2018-01-28 17:59

  本文關(guān)鍵詞： 漸進(jìn)迭代逼近 加權(quán)漸進(jìn)迭代逼近 插值與逼近 加速迭代　出處：《合肥工業(yè)大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：在計(jì)算機(jī)輔助幾何設(shè)計(jì)與逆向工程中,構(gòu)造一組滿足精度要求的曲線(曲面)來插值或擬合給定的有序點(diǎn)集是一類很重要的課題。反求控制頂點(diǎn)的方法往往因?yàn)橛?jì)算量過大(求解大規(guī)模線性方程組)而難以在實(shí)際中推廣,諸多學(xué)者也為此提出了許多不同形式的插值和擬合方法。漸進(jìn)迭代逼近(the progressive iterative approximation,PIA,又稱幾何迭代法)的方法以其良好的自適應(yīng)性和收斂穩(wěn)定性,受到大多數(shù)學(xué)者的青睞,該方法通過不斷調(diào)整與迭代控制頂點(diǎn),得到一組精度不斷提高的曲線(曲面)序列,不僅極大減少了計(jì)算量,而且具有明顯的幾何意義。近年來PIA方法更是在多個(gè)領(lǐng)域得到了廣泛應(yīng)用。經(jīng)典PIA算法雖然能夠保證最后得到的極限曲線曲面插值于給定數(shù)據(jù)點(diǎn),但是前提是要把所有的數(shù)據(jù)點(diǎn)都作為每一步迭代的控制頂點(diǎn)。當(dāng)原始數(shù)據(jù)規(guī)模較大時(shí),經(jīng)典PIA方法就會(huì)出現(xiàn)不夠靈活、迭代速度較慢等不足。近年來涌現(xiàn)的一些改進(jìn)算法有:局部PIA方法、加權(quán)PIA方法、Extended PIA方法、最小二乘PIA方法等,這些方法不斷地?cái)U(kuò)大了PIA方法的適用領(lǐng)域、加快了PIA方法的收斂速率、提高了PIA方法的靈活性,同時(shí)也豐富了PIA方法的內(nèi)容。鑒于PIA方法的類型和諸多優(yōu)點(diǎn),本文主要做了如下工作:1.PIAWPIA1.研究了PIA方法的發(fā)展現(xiàn)狀,對(duì)帶權(quán)漸進(jìn)迭代逼近方法(WPIA)加以改進(jìn),即對(duì)所有的調(diào)整向量取不同權(quán)值,并研究其收斂性及迭代效果;2.對(duì)局部PIA方法進(jìn)行了改進(jìn),實(shí)現(xiàn)了對(duì)要調(diào)整數(shù)據(jù)點(diǎn)的加速迭代,同時(shí)研究了局部PIA方法和局部代數(shù)插值之間的關(guān)系。
[Abstract]:In CAD and reverse engineering. It is an important subject to construct a set of curves (surfaces) that satisfy the precision requirement to interpolate or fit a given ordered set of points. It is difficult to be popularized in practice. Many scholars have also proposed many different methods of interpolation and fitting. The progressive iterative approximation. Bia (geometric iterative method) is favored by most scholars because of its good adaptability and convergence stability. This method controls the vertices by constantly adjusting and iterating. A series of curves (surfaces) with increasing accuracy are obtained, which not only greatly reduces the computational complexity. In recent years, the PIA method has been widely used in many fields. Although the classical PIA algorithm can guarantee the final limit curve and surface interpolation to a given data point. But the premise is that all the data points are used as the control vertices of each iteration. When the original data scale is large, the classical PIA method will appear inflexible. Some improved algorithms have emerged in recent years, such as local PIA method, weighted PIA method and extended PIA method, least square PIA method and so on. These methods expand the application field of PIA method, accelerate the convergence rate of PIA method, and improve the flexibility of PIA method. At the same time, it enriches the content of PIA method. In view of the type and many advantages of PIA method, this paper mainly does the following work: 1. PIAWPIA1.The development status of PIA method is studied. The weighted asymptotic iterative approximation method (WPIA) is improved, that is, all the adjustment vectors are given different weights, and their convergence and iterative effect are studied. 2. The local PIA method is improved to realize the accelerated iteration of the data points to be adjusted, and the relationship between the local PIA method and the local algebraic interpolation is studied.
【學(xué)位授予單位】：合肥工業(yè)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：TP391.7

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1 趙林;帶權(quán)值的漸進(jìn)迭代逼近算法及其應(yīng)用[D];合肥工業(yè)大學(xué);2017年

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本文編號(hào)：1471167