分形维数

基于盒维数法,分析了分形维数量测的各种方法,从二维的盒维数法到三维的立方体覆盖法(CCM)、改进立方体覆盖法(ICCM)、差分立方体覆盖法(DCCM)以及相对差分立方体覆盖法(RDCCM),并解释了各种方法对二维曲线以及三维粗糙面的覆盖原理。其次案例分析了四种三维分形量测方法的异同以及选用原则。最后总结展望了实际工程中分形维数对机械加工、三维重建的指导以及微观分析的辅助作用。

This paper analyses various methods of measuring fractal dimension quantitatively,from two-dimensional box dimension method to three-dimensional CCM cube coverage method,ICCM improved cube coverage method,DCCM differential cube coverage method and RDCCM relative differential cube coverage method,and explains the coverage principle of various methods for rough surface.Secondly,the similarities and differences of the four three-dimensional fractal measurement methods and the selection principles are analyzed.Finally,the guidance of fractal dimension to machining,three-dimensional reconstruction and micro-analysis in practical engineering are summarized and prospected.