Numerical methods to find the slope at a point on map using level curves. Application in road designing

Abstract

The problem of determining the slope at a point on a map using level curves has practical applicability in designing the roads. This problem is reduced to the problem of finding the shortest length segment through a point that connects two coplanar lines. Two methods to solve this problem are presented: a fast approximate method and a slower but exact algorithmic method. The results are compared at the end.

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

“…We present two methods of solving SSTPC2L: an approximate method and an exac mathematical method. These two methods (presented in Sections 2.1 and 2.2) were partially described in [7]. We present two methods of solving SSTPC2L: an approximate method and an exact mathematical method.…”

“…We present two methods of solving SSTPC2L: an approximate method and an exact mathematical method. These two methods (presented in Sections 2.1 and 2.2) were partially described in [7].…”

“…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. Although 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 ultimately related to the embankments optimization.…”