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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.

Heuristic and Numerical Geometrical Methods for Estimating the Elevation and Slope at Points Using Level Curves. Application for Embankments