离散曲面变差的计算
|
摘要
在连续函数变差相关理论基础上,为了更好地描绘实验或实际测得的曲面数据,本文引入离散曲面变差的概念,并提出了离散曲面变差的计算方法。针对两组不同的离散曲面数据,计算它们在不同尺度下的变差以及尺度和变差的双对数图,比较了两组离散曲面的维数与变差关系。研究结果表明:本文提出的离散曲面变差的计算方法是可行的,可以作为计算离散曲面变差的一种方法。
In order to better describe the experimental or actual measured surface data,the concept of discrete surface variation was introduced on the basis of relevant theories of continuous function variation in this paper.The calculation method of discrete surface variation was put forward. In view of the two groups of different discrete surface data,their variations under different scales were calculated,and diagrams of the scale and the variation of double logarithmic were given. The dimensions of the two groups of discrete surface and variation relation were compared. The results show that the method of calculating the discrete surface variation is feasible and can be used as a method of computing discrete surface variation.
In order to better describe the experimental or actual measured surface data,the concept of discrete surface variation was introduced on the basis of relevant theories of continuous function variation in this paper.The calculation method of discrete surface variation was put forward. In view of the two groups of different discrete surface data,their variations under different scales were calculated,and diagrams of the scale and the variation of double logarithmic were given. The dimensions of the two groups of discrete surface and variation relation were compared. The results show that the method of calculating the discrete surface variation is feasible and can be used as a method of computing discrete surface variation.
引文
[1]Tricot C.Curves and Fractal Dimension[M].New York:Spinger-Verlag New York Inc,1995.
[2]Dubuc B,Tricot C.Variation d’une Function et Dimension de son Graph[J].Math Acad Sci Paris Ser:I,1988,306:531-533.
[3]Tticot C.Funtion Norms and Fractal Dimension[J].SIAM J Math Anal,1997,28(1):189-212.
[4]Dubuc B,Zucker S W,Tricot C,et al.Evaluating the Fractal Dimension of Surfaces[J].Proc R Soc Lond Ser:A,1989,425:113-127.
[5]文志英.分形几何的数学基础[M].上海:上海科学技术出版社,2000.
[6]冯志刚,王磊.分形差值函数的变差的性质[J].江苏大学学报:自然科学版,2005,26(1):49-52.
[7]李玲,冯志刚,许荣飞.三维空间中函数图像的计盒维数[J].安徽工业大学学报,2007,24(1):113-116.
[8]Feng Z G.Variation and Minkowski Dimension of Fractal Interpolation Surface[J].J Math Anal Appl,2008,345(1):322-334.
[9]徐惠,冯志刚.一类分形插值函数的变差和计盒维数[J].安徽工业大学学报,2008,25(4):444-447.
[10]黄艳丽,冯志刚.基于二次分形插值函数的分形插值曲面的变差与盒维数[J].河南科技大学学报:自然科学版,2011,32(3):68-71.
[11]黄艳丽,冯志刚.基于分形插值函数的分形插值曲面的变差与计盒维数[J].工程数学学报,2012,29(3):393-398.
[12]Feng Z G,Sun X Q.Box-counting Dimensions of Fractal Interpolation Surfaces Derived from Fractal Interploation Functions[J].J Math Anal Appl,2014,412(1):416-425.
[13]毛北行,孟金涛.离散复杂网络系统的混沌同步[J].郑州大学学报:理学版,2013,45(3):9-12.
[2]Dubuc B,Tricot C.Variation d’une Function et Dimension de son Graph[J].Math Acad Sci Paris Ser:I,1988,306:531-533.
[3]Tticot C.Funtion Norms and Fractal Dimension[J].SIAM J Math Anal,1997,28(1):189-212.
[4]Dubuc B,Zucker S W,Tricot C,et al.Evaluating the Fractal Dimension of Surfaces[J].Proc R Soc Lond Ser:A,1989,425:113-127.
[5]文志英.分形几何的数学基础[M].上海:上海科学技术出版社,2000.
[6]冯志刚,王磊.分形差值函数的变差的性质[J].江苏大学学报:自然科学版,2005,26(1):49-52.
[7]李玲,冯志刚,许荣飞.三维空间中函数图像的计盒维数[J].安徽工业大学学报,2007,24(1):113-116.
[8]Feng Z G.Variation and Minkowski Dimension of Fractal Interpolation Surface[J].J Math Anal Appl,2008,345(1):322-334.
[9]徐惠,冯志刚.一类分形插值函数的变差和计盒维数[J].安徽工业大学学报,2008,25(4):444-447.
[10]黄艳丽,冯志刚.基于二次分形插值函数的分形插值曲面的变差与盒维数[J].河南科技大学学报:自然科学版,2011,32(3):68-71.
[11]黄艳丽,冯志刚.基于分形插值函数的分形插值曲面的变差与计盒维数[J].工程数学学报,2012,29(3):393-398.
[12]Feng Z G,Sun X Q.Box-counting Dimensions of Fractal Interpolation Surfaces Derived from Fractal Interploation Functions[J].J Math Anal Appl,2014,412(1):416-425.
[13]毛北行,孟金涛.离散复杂网络系统的混沌同步[J].郑州大学学报:理学版,2013,45(3):9-12.