Mathematical formulation and preliminary testing of a spline approximation algorithm for the extraction of road alignments

• Roadway planning requires the road axis to be defined in terms of alignments.
• A new method to identify road alignments uses splines to model roads.
• The road is divided into alignments depending on its curvature.
• Values of the obtained relative errors in road parameters are small.

This paper presents a methodology that allows the identification of the road alignments (curves, straights and clothoids) and their corresponding values of curvature based on a list of points with UTM coordinates obtained from field data. The procedure reconstructs the geometry of a road using a cubic spline that gives the road's singular points, geographically referenced, with the curvature values for each element. The methodology allows the user to select different parameters depending on the road type analyzed. It was applied in almost 1500 km of road with satisfactory results. The results of applying the methodology on a recently built road (whose alignments according to its project are known) are shown. A comparison of the project alignments with the alignments obtained according to the proposed method gives good results with small errors relative values, with maximum values of less than 4%.