双参数细分曲线曲面的构造方法研究

【作者】 邹冬花；

【导师】 韩旭里；

【作者基本信息】 中南大学 ， 计算数学， 2006， 硕士

【摘要】 细分法是计算机辅助几何设计中一个很重要的方法，是曲线曲面的离散化造型方法，是根据初始数据由计算机直接生成曲线曲面或其他几何形体的一类方法。随着计算机图形学和几何造型技术的发展，细分方法得到了广泛和深入的研究，目前出现了很多细分方法，如Chaikin算法、四点插值细分算法、de Boor算法和Catmull-Clark细分法等。本论文在这些细分法的基础上研究了一类新的双参数的细分曲线和双参数的细分曲面。双参数的细分曲线。在双参数的细分曲线中讨论了插值的细分曲线和逼近的细分曲线两种，这两种细分曲线都是通过在曲线细分过程中引入两个参数，给出一种新的插值的细分曲线构造的方法，使得所得的细分曲线可调。通过调节一个参数值，可以得到一族插值的细分曲线。另一个参数是细分过程的改变参数，改变它的初值，也可得相应的细分结果。文中分析了细分规则的收敛性和连续性。最后给出了曲线设计的实例，表明所给算法是简单有效的。双参数的细分曲面。通过在曲面细分过程中引入两个参数，给出一种新的细分曲面构造的算法，使得所得的细分曲面可调。通过调节一个参数值，可以得到一族细分曲面。另一个参数是细分过程的改变参数，改变它的初值，也可得细分结果。最后也给出了曲面设计的实例，表明这种算法简单、有效。更多还原

【Abstract】 Subdivide Scheme is a very important method of computer aided geometric design ,is a method for discrete modelling of curves and surfaces, is a method ofgenereting curves and surfaces or other geometric figure directly by computer based on initial datas .With the development of computer graphics and geometric modeling, subdivide scheme has been widely and deeply studied ,at present ,many subdivide schemes have appeared such as Chaikin method、4-point interpolatory subdivision scheme、de Boor method and Catmull-Clark skill.Based on these subdivide schemes ,this thesis studies a new class of two-parameters subdivision surfaces and subdivision curves.The two-parameters subdivision curves. Interpolatory subdivision curves and approximation subdivision curves are discussed in the two-parameters subdivision curves. A new algorithm to design adjustable subdivision curves using two control parameters is presented in the two subdivision scheme. A kind of subdivision curves can be constructed by changing one of the parameters. Meanwhile , the shapes of the subdivision curves can be adjusted by using the another control parameter. The convergence and continuity of the subdivision scheme are analyzed. Some examples of the curve design are given to demonstrate the freedom and efficiency of the algorithm. The two-parameters subdivision surfaces. A new algorithm to design adjustable subdivision surfaces using two control parameters is presented in this paper. A kind of subdivision surfaces can be constructed by changing one of the parameters. Meanwhile , the shapes of the subdivision surfaces can be adjusted by using the another control parameter.Some wxamples of the curve design are given to demonstrate the freedom and efficiency of the algorithm.更多还原