二重细分法的研究

发布时间：2018-05-08 17:06

本文选题：有理细分法 + C~k连续性　；参考：《合肥工业大学》2017年硕士论文

【摘要】：细分方法是一种从初始控制多边形出发,通过不断的迭代最终生成光滑曲线曲面的方法,其凭借着算法简单和易实现的优点在几何造型中得到了广泛的应用。本文首先介绍了曲线细分的基本原理,之后提出了一些曲线细分方法。首先,本文提出了一种有理的二重四点逼近细分格式,并分析了该格式的收敛性和连续性,在该格式中通过对参数取特殊值得到了一个具有保形性的细分格式,对于一些没有尖角的图形,它所生成的极限曲线非常接近初始控制多边形。其次,由于通常都用Laurent多项式来表示细分的生成多项式,根据两者之间的关系,本文提出了一个多参数的Laurent多项式,此多项式能够生成很多已有的经典格式,还可以构造非对称细分。本文不但研究了由该多项式得到的四点细分格式和五点细分格式的收敛性和连续性,而且针对五点细分格式,比较了特殊情况下对称细分与非对称细分生成极限曲线的逼近效果。
[Abstract]:Subdivision is a method to generate smooth curves and surfaces through continuous iteration from the initial control polygon. It is widely used in geometric modeling by virtue of its simple and easy implementation. This paper first introduces the basic principle of curve subdivision, then puts forward some curve subdivision methods. First of all, this paper presents a rational double quadrilateral approximation subdivision scheme, and analyzes the convergence and continuity of the scheme. In this scheme, a conformal subdivision scheme with conformal property is obtained by taking special parameters. For some graphs with no sharp angle, the limit curve generated is very close to the initial control polygon. Secondly, because the generative polynomials of subdivision are usually represented by Laurent polynomials, according to the relationship between them, this paper proposes a multi-parameter Laurent polynomial, which can generate many classical forms. Asymmetric subdivision can also be constructed. In this paper, we not only study the convergence and continuity of the four-point subdivision scheme and the five-point subdivision scheme obtained from the polynomial, but also study the five-point subdivision scheme. In this paper, the approximation effect of the limit curve generated by symmetric subdivision and asymmetric subdivision is compared.
【学位授予单位】：合肥工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP391.7

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