一种利用反S数学模型自动确定地图目标分形无标度区的新方法(英文)  

A New Method to Determine Fractal Non-scaling Interval of Map Objects Automatically Based on Inverse 'S' Mathematical Model

作　　者：蔡金华 龙毅[2] 毋河海[3] 陈丹 

机构地区：[1]国家智能交通系统工程技术研究中心,北京100088 [2]南京师范大学地理科学学院,江苏南京210097 [3]武汉大学资源与环境科学学院,湖北武汉430079 [4]北京四维图新导航信息技术有限公司,北京100083

出　　处：《测绘学报》2006年第2期177-183,190,共8页Acta Geodaetica et Cartographica Sinica

基　　金：国家自然科学基金项目(49971068205160635)

摘　　要：在观测尺度r的取值范围足够大时,地图目标的Richardson曲线往往呈现反S形态。根据这一特点,采用反S数学模型———带导数三次多项式模型拟合Richardson曲线,并根据该模型推导出分形无标度区间的计算公式,提出一种自动确定地图目标分形无标度区的新方法,最后通过实验验证本方法的可行性和有效性。If the scaling range of observing is large enough, the Richardson curve of a map object always has an inverse ogee shape. Considering this fractal character of map objects, this paper analyzed why this phenomenon appeared in detail, and proposed a new method for determining the fractal non-scaling interval of a map object. This new method substitutes an inverse ‘S＇ mathematical model-Cubic Polynomial Model with Derivative for the original Richardson curve of a map object. On the base of the mathematical model, a mathematical formula for determining the non-scaling interval was established. Finally some typical experiments validated the great efficiency of the new method.

关 键 词：分形 无标度区 Richardson曲线 反S数学模型 地图目标 

分 类 号：P283[天文地球—地图制图学与地理信息工程]