一种基于傅里叶变换的光滑边界面状要素Morphing方法

A Morphing Method for Smooth Area Features Based on Fourier Transform

提出一种基于傅里叶(Fourier)变换的光滑边界面状要素Morphing方法。针对同名面状要素在两个不同比例尺下的表达,利用Fourier变换将多边形在空间域的矢量坐标串表达形式转换为频率域的函数表达形式,然后对二者的Fourier函数进行复合得到多边形在任意中间尺度的表达函数,最后将中间状态的Fourier函数展开为矢量坐标串表达形式获得多边形的中间插值形状。实验证明,该基于Fourier变换的面状要素Morphing方法,能在保持形状特征的基础上对于边界光滑的多边形要素实现光滑、连续的多尺度表达。

A Fourier transform based morphing of smooth area features is presented in this paper.For the two vector representations of the same feature on the source and destination scales,their shape descriptions of coordinate string on space domain are converted to the description by mathematical function on frequency domain based on Fourier transform.Then the function at intermediate scale is calculated by the weighted mixed on the source and destination function,and the shape in vector at intermediate scale is restructured by inverse Fourier transform.The experiments show that the Morphing method of smooth area feature can preserve the original area feature＇s geometry characteristics and get smooth and continuous multi-scale representations of vector polygon.