【作者】 李红；

【导师】 顾耀林；

【作者基本信息】 江南大学 ， 计算机应用技术， 2005， 硕士

【摘要】 随着计算机辅助几何设计(CAGD)与图形学的发展,几何造型技术在许多领域得到了广泛的研究和应用,其中关于曲线曲面的生成效率和生成效果一直是其中很重要的内容。本文针对这两个方面,主要研究了曲线曲面快速逐点生成算法和曲面的保形技术,并提出了两个新的方法。曲线曲面逐点生成的一个关键性因素就是迭代次数的选取,即步长的选取。步长过短,则会导致取点过密,造成重复绘制的问题,从而降低了绘制效率;取点过长,造成曲面不连续问题,则会降低曲面的生成效果。本文的方法是通过引入导矢界的概念,利用曲面的导矢界,来更加精确的估计迭代次数n值的选取,改进了曲面快速逐点生成中的n值,即增加了步长,这样有效的解决了曲面绘制中出现的重复绘制的问题,改进了曲面的生成效率,在此基础上,也能保证曲面的生成效果。通过实例表明,进一步提高了曲面绘制的效率和效果。本文还研究了曲面保形技术,构造了一类能够保单调的均匀α-B样条插值曲线,通过改变其中的参数α值,来调整曲面的形状。然后利用该曲线在xy方向进行插值,来保证曲面的形状。利用这类曲线进行插值可以得到较好的保形效果,易于在工程实践中获得广泛的应用。更多还原

【Abstract】 With the development of computer graphics and CAGD, geometry modeling is an important research field in the computer graphics. The generating efficiency and the effect of the surfaces is always very important part. This thesis not only reviews the technology of the Point-to-Point generating surfaces and surfaces preserving ,but also presents two new methods.The important factor of the Point-to-Point generating surfaces algorithm is how to choose the iterative steps. If your choice is too big, we will have to deal with too many points. In this case, it induces the problem of the repletion and reduces the efficiency. If your choice is too small, it will reduces the effect of the surfaces. In this paper, Some new formulae for the derivative bounds of surfaces are presented, based on the derivative bounds of surfaces, some formulas for the derivatives bounds of surfaces are presented. Using these formulas, it is better to solve the problem of repetition and discontinuity and much effective to rendering the surfaces.The surfaces preserving methods have been presented in this paper. In this paper, the monotonicity-preserving interpolation of a kind of plane parameter curve with a shape control parameter is investigated. Using this kind of curve, the monotone-preserving interpolating surfaces can be obtained succinctly. It can be widely used in project.更多还原