Calculation of the available 3-d sight distance by modeling the roadway as a 3-d B-spline surface

The objective of this paper is to develop a mathematical methodology that allows the available sight distance calculation of a roadway directly in three-dimensional space and in a fully automatic and accurate manner. The presented methodology overcomes the conventional approach of studying the three-dimensional roadway configuration separately and sequentially in its horizontal and vertical alignment. As far as the road surface is concerned, it is simulated as a 3-d B-spline surface with continuous side barriers whose road centerline has been in turn, simulated as a 3-d B-spline curve. Through this approximation, the road centerline as well as the right and left borderlines which play a crucial role in the sight distance calculation are mathematically defined both geometrically and analytically. The sight distance calculation can be made in each point of the road surface, due to the integrated information existing in the model through its three-dimensional character. These calculations are clearly more reliable, since they are applied on a realistic 3-d road surface. It is worth mentioning that this methodology can be applied on existing roads as well as during the design process by modifying the pseudogeodesic and/or pseudonormal curvature of the roadway in order to obtain the desired available sight distance. Finally, the computational part of this methodology is attained by expressing all the functions and algorithms in code through the programming language offered by the software Mathematica, whereas the whole process is demonstrated as a case study accompanied by Figures and Tables.