Hermite-Shannon-Cosine区间小波及其在图形自适应分划插值中的应用

Hermite-Shannon-Cosine Interval Wavelet and Its Application in Adaptive Distribute Interpolation on Curves

动态曲线图是描述客观现象变换规律的常用工具,为实现动态曲线特征点的动态捕捉及精确表达,构造了同时具有插值性、光滑性、紧支撑性和对称性的Shannon-Cosine小波函数.首先利用Shannon小波函数的波动性和连续性,根据积分中值定理,设计了一种参数化的窗函数,通过参数调整,可满足Shannon-Cosine小波对支撑区间和光滑度的自适应控制的要求;其次,分析确定了对曲线进行小波变换时边界效应归因于曲线边界的不连续,因此,采用2点3次Hermite插值函数构建了区间小波;最后,采用多尺度Shannon-Cosine小波对冲击波传播曲线和反射Burger曲线进行多尺度自适应细分和逼近,自动捕捉曲线的特征点进行重构.实例结果表明,与其他方法相比,Hermite Shannon-Cosine区间小波逼近曲线具有较高的数值精度和较低的算法复杂度.

The dynamic curve is a common tool to describe the transformation law of various phenomena.To capture the characteristic points dynamically and approximate the dynamic curve accurately,a Shan-non-Cosine wavelet function with interpolation,smoothness,tight support,and symmetry is constructed.Firstly,by means of the wavelike property and continuity of the Shannon wavelet function,a parameterized window function is designed based on the integral median theorem,in which the support and smoothness of Shannon-Cosine wavelet can be chosen to meet the requirement of the approximated curves.Secondly,based on the theory analysis and numerical experiments,the discontinuity near the boundary of the curve is identi-fied as the major factors which result in the boundary effect appeared on the wavelet transform on the curve,and then the interval wavelet is constructed by using the two-point cubic Hermite interpolation function.Fi-nally,the multi-scale Shannon-Cosine wavelet is used to perform multi-scale adaptive subdivision and ap-proximation of the propagation of shock wave curve and the reflected Burger curve.It is able to capture the characteristic points of the curve adaptively,which can be used to reconstruct the curve.Burger curve is taken as the example to test the proposed method,the numerical experiments show that,compared with other methods,the method of Hermite Shannon-Cosine interval wavelet approximation curve has higher numerical accuracy and lower algorithm complexity.