文章摘要
集逼近插值于一体的形状可调曲线曲面
Shape adjustable curves and surfaces integratingapproximation and interpolation
  
DOI:
中文关键词: B样条曲线曲面  逼近与插值  分段组合  形状参数
英文关键词: B spline curve and surface  approximation and interpolation  piecewise combination  shape parameter
基金项目:国家自然科学基金资助项目(11261003;11761008;11771453);江西省自然科学基金资助项目(20161BAB211028);江西省教育厅科技项目(GJJ160558)
作者单位
严兰兰1,2,韩旭里2,樊继秋1 1.东华理工大学 理学院,江西 南昌 3300132.中南大学 数学与统计学院, 湖南 长沙 410083 
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中文摘要:
      为了使3次均匀B样条曲线曲面既可以在不改变控制顶点的情况下自由调整形状,又可以在不需要反求控制顶点的情况下轻松实现插值,这里在多项式函数空间上构造了含两组参数的混合函数,并由之定义了基于四点分段的多项式曲线和相应的张量积曲面.混合函数以3次均匀B样条基函数为特例.其中的一组参数控制曲线段的端点位置、曲面片的角点位置;另一组参数控制曲线段在端点处的切矢、曲面片在角点处的切矢.合理选择参数,可以使曲线曲面位于控制顶点的凸包内,或者插值内控制顶点.因此,这里用一个模型实现了对控制多边形或控制网格进行逼近和插值的统一表示.数值实验结果显示了方法的正确性与有效性.
英文摘要:
      Two main goals were tried to realize. One was to make the shape of the cubic uniform B-spline curve and surface can be adjusted freely under the condition of without changing the control points. The other was to make the curve and surface can easily achieve interpolation in the case of did not need to reverse compute control points. To achieve these aims, a kind of blending function, which contains two groups of parameters, was constructed in the polynomial function space. Based on the blending function, the polynomial curves were defined, which on four-point piecewise scheme and the corresponding tensor product surfaces. The blending function contained the cubic uniform B-spline basis function as a special case. One set of parameters of the blending function determine the endpoint position of the curve and the corner point position of the surface. While another set of parameters control the tangent vector of the curves at the endpoints and of the surfaces at the corner points. By choosing appropriate parameters, the curves and surfaces were located within the convex hull of the control points, or interpolate the inner control points. As a result, with only one model, the uniform representation is achieved, which of the curves and surfaces for approximating and interpolating the control polygon and control net. The numerical experimental results show the correctness and effectiveness of the method.
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