Abstract
Both the calculation of ground slopes at points on the map and the elevation estimation for these points bear significant importance and also have applications in various domains, such as civil engineering, road and railway design. The paper presents two methods that use level curves: one that is fast and approximate and another which is slower, but more precise. The running speed of the two proposed methods and their results are compared by performing 100 million experiments. The paper also presents how these methods can be applied to optimize embankments. An accurate method to calculate the horizontal plane of the excavation/filling when building a new house is also presented.
Highlights
The possibility of calculating the slope and elevation using level curves has practical applicability in several fields of activity, such as civil engineering [1], architecture [2,3], railway [4], road and bridge engineering [5,6,7,8], topography [9], etc
The results found can be used in various areas, this article is limited to solving two problems related to civil engineering and to railways, roads, and bridges, both related to the embankments optimization
The current article presents a rigorous and mathematically accurate solution to find the optimum between excavations and fillings, resulting in a reduction of the embankments related costs
Summary
The possibility of calculating the slope and elevation using level curves has practical applicability in several fields of activity, such as civil engineering [1], architecture [2,3], railway [4], road and bridge engineering [5,6,7,8], topography [9], etc. This problem is reduced to estimating the shortest segment that connects two lines through a point. Tcwomopmaertehdo.dTso afrienpalriozpeothseedpanpderd, icsocnucslsuesdioinsSwecitlliobne 4d,rwawhenrebatsheedy oanrethcoemarpgaurmede.nTtos pfirneasleiznetetdh.e paper, conclusions will be drawn based on the arguments presented
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