【作者】 范自柱；

【导师】 檀结庆；

【作者基本信息】 合肥工业大学 ， 计算机软件与理论， 2003， 硕士

【摘要】 近年来，二维物体渐变技术在工业模拟、虚拟现实、科学计算可视化、生物医学工程、广告娱乐等领域获得了快速的发展。这种技术主要包括两方面内容：二维形状渐变和图象渐变技术。二维物体渐变技术实现方法多种多样，目前提出的算法各有优缺点，无论是形状渐变算法，还是图象渐变算法，它们中的大多数都是处理两个物体之间的渐变。在本文中，利用连分式理论，提出了一种在多个二维物体之间进行渐变的算法。首先，本文对二维物体渐变技术作了详尽的讨论，介绍了它的两方面内容。一是二维形状渐变的基本方法，在这一部分中，着重讨论了多边形的渐变方法；二是图象渐变，在阐述了它的主要算法和成熟的方法后，详细介绍了一种在多幅图象间进行渐变的方法，并对此进行分析。其次，在本文的第二章，系统地论述了连分式的基本原理和应用方法，尤其是对Thiele型连分式插值函数作了具体的讨论，因为，它是在实验中所用到的主要的插值工具。最后，本文的结尾，给出连分式应用于二维物体渐变的实验过程和结果，并对其进行了仔细的分析和讨论。实验表明，把连分式用在二维物体的渐变过程中，取得了不错的效果，是成功的。更多还原

【Abstract】 In recent years,the technology of 2D object metamorphosis has got rapid development in the field of industrial simulation,virtual reality,scientific computing visualization, biomedicine project, advertising and entertainment and so on.This technology principally consists of two parts:2D shape morphing(blending) and image morphing(or metamorphosis). There are a lot of methods of 2D object metamorphosis.The current algorithms have advantages and disadvantages.Whether the shape morphing algorithms or image morphing algorithms are concerned,most of them deal with the morphing between two objects.In this thesis, an algorithm of the morphing among multiple 2D objects is presented with the aid of theory of continued fractions.First,the technology of 2D object metamorphosis is discussed in detail and two main parts are presented in this thesis.In the first part are the principal methods of 2D shape blending. And in this part,the algorithm of polygons is emphasized.The second part is focused on image morphing.After expatiating its principal algorithms and mature methods,a method among multiple images is presented and analysed in detail.Second,in the second chapter of this thesis,the basic theories and methods are systematically discussed ,especially Thiele continued fractions,because it is the main interpolation tool in the experiments.And finally,the processes and results of experiments in the application of continued fractions to 2D object metamorphosis are given,and detailed analyzing and discussing are made.The experiments show that the results are good .This demonstrates that it is successful for continued fractions to be applied in the processes of 2D object metamorphosis.更多还原