Positive blending Hermite rational cubic spline fractal interpolation surfaces
Positive blending Hermite rational cubic spline fractal interpolation surfaces
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DOI：
10.1007/s10092-013-0105-5
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发表时间：
2014-01
期刊：
影响因子：
1.7
通讯作者：
A. Chand;N. Vijender
中科院分区：
文献类型：
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作者：
A. Chand;N. Vijender
分形插值提供了一种有效的方法来描述具有光滑和非光滑结构的数据。基于分形插值函数理论，构造了Hermite有理三次样条分形插值函数（分形边界曲线），使其沿插值域的网格线沿着逼近原函数.然后利用这些分形边界曲线生成混合Hermite有理三次样条分形插值曲面。研究了Hermite有理三次样条FIS对原函数的收敛性。对分形边界曲线中涉及的比例因子和形状参数进行了适当的约束，使得只要沿网格线沿着给定的插值数据为正值，这些分形边界曲线就为正值。当相应的分形边界曲线为正值时，我们的Hermite混合有理三次样条FIS为正值。各种集合的分形边界曲线可以适应与适当的修改，在相关的缩放参数或/和形状参数，因此，我们的建设允许互动的合理FIS的形状改变。
Fractal interpolation provides an efficient way to describe data that have smooth and non-smooth structures. Based on the theory of fractal interpolation functions (FIFs), the Hermite rational cubic spline FIFs (fractal boundary curves) are constructed to approximate an original function along the grid lines of interpolation domain. Then the blending Hermite rational cubic spline fractal interpolation surface (FIS) is generated by using the blending functions with these fractal boundary curves. The convergence of the Hermite rational cubic spline FIS towards an original function is studied. The scaling factors and shape parameters involved in fractal boundary curves are constrained suitably such that these fractal boundary curves are positive whenever the given interpolation data along the grid lines are positive. Our Hermite blending rational cubic spline FIS is positive whenever the corresponding fractal boundary curves are positive. Various collections of fractal boundary curves can be adapted with suitable modifications in the associated scaling parameters or/and shape parameters, and consequently our construction allows interactive alteration in the shape of rational FIS.