李长明. 在等高线地形图上量算表面积各种方法的分析、比较和改进[J]. 武汉大学学报 ( 信息科学版), 1980, 5(2): 72-87.
引用本文: 李长明. 在等高线地形图上量算表面积各种方法的分析、比较和改进[J]. 武汉大学学报 ( 信息科学版), 1980, 5(2): 72-87.
Li Changming. Analysis,Comparision aid Improvement of the Method of Measuring Land Surface Area on Topographical Maps[J]. Geomatics and Information Science of Wuhan University, 1980, 5(2): 72-87.
Citation: Li Changming. Analysis,Comparision aid Improvement of the Method of Measuring Land Surface Area on Topographical Maps[J]. Geomatics and Information Science of Wuhan University, 1980, 5(2): 72-87.

在等高线地形图上量算表面积各种方法的分析、比较和改进

Analysis,Comparision aid Improvement of the Method of Measuring Land Surface Area on Topographical Maps

  • 摘要: 在等高线地形图上量算面积的方法已有五种之多,在文献3中曾着重在繁简方面对各种方法作了详细的比较,但未指出各种方法的内在联系,也没有比较各种方法所得结果在怎样的程度上逼近表面的真实面积。本文首先由面积的基本公式和近似计算的原理,指出各种方法的来源和其间的相互关系,並导出了这些方法所算得数值之间的不等式,同时又在逼近真实面积的程度上比较了各种方法的优劣。接着用初等方法,研究了各种渐近值对怎样的表面才趋于真实面积,从而使其在实际应用时,能据此选出最合理的计算公式。其次,利用证明上述问题的方法,提出了简化计算的图解法。使精确性最高但计算繁难的华罗庚、王元方法变得简易可行。最后,根据同样的原理提出了一组新的公式,並与原公式相比,证明了新方法具有同等的精确性,而且省略了在地形图上量测面积的过程,因此在没有求积仪的情况下,就显示出了新方法的实用价值。

     

    Abstract: There are five methods of measuring land surface area on topographical maps.A paper 3 has made a detailed comparision between the complicateness of the various methods;it has,however,not indicated their internal relationships nor made a comparision between the results obtained by the various methods,as to what extent they approach the actual surface area.The author of the present paper attempts to prove by the fundamental formula of area and the principles of approximate calculation the mutual relationships between the various methods;accordingly,derives the non-equality between the values obtained by them and at the same time,compares their merits and defects according to their approximation to the actual area.Furthermore,the author makes a study by elementary method of the closeness of different asymmptotic numeral values to the actual area for ditffterent shapes of surface,which enables us to choose the most reasonable formulae of calculation in practice.Then,the author suggests a graphical method,based on the same principle of he above analysis,which simplifies the calculation work of the most accurate but more complicated Hua Lokeng and Wang Yuan s method.Lastly,based on the same principle,the anthor derives a set of new formulae,which are as accurate as the existed fomulae,but do not require the process of area on topographical maps.Hence they are especially useful in case of having no planimeter.

     

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