基于细分曲面的含参离散造型算法  

Discrete Modeling Algorithms Based on Subdivision Surfaces with Parameters

作　　者：杨军[1] 郝伶[1] 

机构地区：[1]南昌航空大学,江西南昌330063

出　　处：《南昌航空大学学报（自然科学版）》2012年第3期28-34,共7页Journal of Nanchang Hangkong University(Natural Sciences)

基　　金：国家自然科学基金(51065024);国家自然科学基金天元基金(11126338);江西省教育厅青年科学基金(GJJ11177)

摘　　要：为增加几何造型算法的灵活性,在细分模板中引入参数,利用生成函数考察细分法能够产生光滑曲线所需条件,得到一类含参曲线细分算法;通过对模板进行张量积并推广到任意拓扑结构网格,得到含参C1可调细分曲面算法;利用曲线模板,自然构造出对开网格所需的边界条件;利用特征分解技术分析了奇异点处的光滑性,得到参数范围;造型实例表明,每一种算法均能在对应情况下达到调控形状的要求.To increase the flexibility of a geometric modeling algorithm,parameters are introduced into the masks of the subdivision algorithm.The smoothness condition for the algorithm is discussed in terms of the generating function and a curve with a parameter is obtained.By applying the tensor product construction technique to subdivision masks,adjustable subdivision surfaces of arbitrary topology with one parameter are obtained.In addition,boundary conditions for open mesh are also derived naturally by making use of the masks of curves.The convergence property at an extraordinary vertex is studied by using the eigendecomposition techniques.Modeling examples show that the algorithm is able to meet the requirements of shape adjustment.

关 键 词：样条 参数 离散造型 生成函数 张量积 细分曲面 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]