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.