【作者】 詹棠森；

【导师】 苏化明；

【作者基本信息】 合肥工业大学 ， 计算数学， 2003， 硕士

【摘要】 本文论述了二个方面的内容：一是组合参数曲线的变形。二是组合参数曲线的磨光。对于贝齐尔曲线，由于它采用一组独特的基函数，所以它具有良好的优良性质。在实践中，它表现了强大的生命力，用途广泛。 另外，我们经常会遇到一个普遍问题，就是难以用单一的贝齐尔曲线段描述复杂的形状。贝齐尔方法对形状的定义是整体方案，欲对其作局部修改，必然会影响到整体，即贝齐尔方法是有整体控制性质，但却缺乏局部控制性质。通过任意分割和任意升阶得出所要变形的一段，以及增加控制点，增加对曲线进行控制的潜在灵活性。这篇论文讨论贝齐尔曲线局部自由变形的问题。结果是使变形的曲线可以不断进行变形，得到所需的图形。然而，无论是基于伸缩因子的自由变形还是基于任意分割参数曲线的自由变形都会使参数曲线的光滑度降低。这样，本文又讨论了参数曲线的光滑变形问题，解决的方法就是通过参数曲线的磨光法实现参数曲线的光滑度。 综上所述：本论文的目的就是讨论组合参数曲线的自由光滑拼接。更多还原

【Abstract】 The thesis discusses two respects of contents: One is deformation of combination of parametric curve.The other is smoothing of combination of parametric curve.Bezier curve has good character ,because it uses a sequnce of special basic function . Bezier curve has strong ability in practice and is widely used .In addition ,we often encounter a general problem-it is very difficult to describe a complex shape with a single Bezier curve precise .Method of Bezier definites shape of curve ,which is global project .If you locally modify curve ,it is necessary to affact the global .It is that method of Bezier has character of global control,but it has not charater of local control .By way of arbitrary partition .arbitrary degree elevation ,that may increases control point .increases potential active character of controling curve.Therefore, the thesis discusses mainly the problem of local free-form deformation ,which may make Bezier curve deform continuely and gain wanted figures.However, no matter what free-form deformation based on extension factor for parametric curve or arbitrary partition will reduce smoothness of parametric curve. Therefore.the thesis discusses the problem of smooth deformation parametric.Solving method is to realize smooth merging of parametric curve by smoothing parametric curve.To sum up ,the purpose of the thesis is that it discusses freely-smooth merging of combination.更多还原