【作者】 张晓军；

【导师】 彭兴璇； 崔利宏；

【作者基本信息】 辽宁师范大学 ， 计算数学， 2011， 硕士

【摘要】 在计算机辅助几何设计中,过渡曲面的构造是一个重要的研究课题,所谓的过渡曲面是指曲线或曲面间的具有一定连续性的过渡面。也就是说对于给定的两片或多片曲面以及原曲面上的边界线,怎样来构造一个曲面,让这个曲面与原曲面之间在边界线处光滑连接。因为它在汽车,船舶,飞机等工业制造领域的强实用性,所以就成为计算机辅助几何设计(CAGD)的一个重要学术分支。本文总结了一些学者构造过渡曲面的方法,并对这些方法经行了分析与研究,在分析过程中发现,这些方法可分为参数形式研究和隐式形式的研究,对比这两种方法,很容易发现参数形式更容易画图,细分,约束或者是说更容易去调整曲面的形状,而隐式形式则很容易确定过渡曲面与原曲面之间的连续性,使其能很容易达到想要达到的连续性。如果我们选择其中一种形式而另一种形式的优点则减弱,因此能提出一种两种形式优点相结合的方法是一个很重要的研究课题,这就要求我们在研究构造方法中既要满足一定的连续性又要满足灵活的调整性。通过分析对比本文提出了一种新的方法。因为所要构造的过渡曲面是由一束空间曲线构造而成,而空间曲线是由原始曲面上的点与调控线上的点插值构成的B-样条参数曲线,所以称它为B样条曲线构造法,并且用这个方法构造的过渡曲面能和原始曲面达到G 1连续。又因为这个过渡曲面具有参数形式所以它的形状很容易用参数因子和调控线去控制。文中最后通过一些例子展现了这种方法的灵活性与有效性。更多还原

【Abstract】 In engineering design and geometric modeling process, how to construct a blending surface among several curves or surfaces is an important problem in the CAGD, which is to construct a blending surface that smoothly joins two or more given curves or surfaces. That is, for given two or several surfaces and those blending borders, how to construct a blending surface which contacts original surfaces as high order continuity as possible. Because it has strong practicability in automobile, airplane, shipping and other industrial manufacturing field, so it become an important academic branch of computer aided geometric design (CAGD).This paper summary, analysis, research some methods which other researchers construct blending surface,and find as many construction of blending surface methods, surface can be classified into two types: one of the implicit surfaces, another is parametric surfaces .In comparing the two types of surfaces one notes that parametric surfaces are generally easier to draw, subdivided and bound, or easier to adjust the shape of blending surface whereas an implicit surface is easily determine the continuity between the blending surface and the original surface, make it can easily achieve satisfactory continuity. If we choose one kind of form and another form advantages is abate. So it is an important research fields to combine with the two forms advantage. This requires that we research the construction methods to satisfy some continuity but also to satisfy the flexible adjustment.Through the comparative analysis, this paper put forward a new method. Because the blending surface is constructed with a collection of space curves, which are defined by points on the blending boundaries of primary surfaces and the points on the given adjustment curves. The iso-parametric curves are B-Spline curves, which interpolate the blending boundaries. So we call it B-spline curves constructing method. And the constructing method that smoothly joining two or more surfaces with G 1 continuity. Because the blending surface has a parametric form, so its shape is easy to be controlled by adjusting the parameters and adjustment curves. In the end of this paper several numerical examples are presented to show the feasibility and validity of our method.更多还原