双变量有理样条分形插值的单调数据可视化  

Bivariate Rational Cubic Spline Fractal Interpolant for Monotone Data Visualization

作　　者：张余娟 包芳勋[1] Zhang Yujuan;Bao Fangxun(School of Mathematics, Shandong University, Ji’nan 250100)

机构地区：[1]山东大学数学学院,济南250100

出　　处：《计算机辅助设计与图形学学报》2017年第5期882-894,共13页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(61672018);山东省自然科学基金(ZR2015AM007)

摘　　要：对传统的多项式分形插值而言,保持给定形状数据的性质是一项困难的工作.为了使分形插值曲面具有保形性,提出一种有理分形曲面插值方法.首先在传统双三次有理埃尔米特样条插值的基础上构建一种有理样条分形插值函数,它可以用对称的基函数和简单的矩阵形式表示,并且由于形状参数的嵌入使得分形曲面的形状具有局部可调性;然后通过对尺度因子和形状参数的约束,提出一种保单调的分形曲面插值系统.实验结果表明:文中提出的有理分形曲面具有很好的拟局部性,能够保持给定单调数据的形状性质,在图像处理的应用中取得了较好的主客观效果.A novel method of constructing C1rational fractal surfaces is developed with the help of classicalbi-cubic rational Hermite interpolation,which provides a unified approach to the fractal generalization of various traditional bivariate rational spline interpolation.Compared with the existing fractal interpolation,this kind of rational spline fractal interpolation has the following advantages:1)The construction of bivariate rational fractal interpolation functions(BRFIFs)described here allows us to embed shape parameters within the structure of differentiable fractal functions,so that it is more flexible and diverse than the current interpolation.2)It can be explicitly expressed by the symmetric bases and the simple matrix form.3)The shape of the fractal interpolation surfaces can be modified by selecting suitable parameters for the unchangedinterpolating data.In order to meet the needs of practical design,a monotonicity-preserving fractal surface interpolating scheme is developed to visualize monotonic data in the view of monotone surfaces by using constraints on scaling factors and shape parameters in the description of the BRFIFs.The experimental results demonstrate that the proposed model achieved competitive performance,not only subjectively but also objectively.

关 键 词：有理样条 分形插值 曲面造型 数据可视化 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]