Generic Methodology for 3-D Available Sight Distance Calculation

The objective of this paper is to develop a generic mathematical methodology that can carry out the available sight distance calculation of a roadway directly in 3-D space and in a fully automatic manner. The presented methodology overcomes the conventional approach of studying the 3-D road configuration separately and sequentially in its horizontal and vertical alignment. As far as the road surface is concerned, it is modeled as a 3-D B-spline surface. Moreover, the road centerline as well as the right and left borderlines which play a crucial role in the sight distance calculation are mathematically defined by modeling them as 3-D B-spline curves; therefore, their mathematical formulation is well determined. In addition, the cut and fill slopes of the road are also modeled as 3-D surfaces, and finally, the road surface and its corresponding cross sections are realized as one strictly defined and unified 3-D mathematical surface. This is particularly important since integrated 3-D geometric information is obtained, meaning that all calculations are applied in the real 3-D space where the road construction actually exists. Eventually, all the concepts that are incorporated in the respective equations and formulas are applied in the natural 3-D geometry of the road surface. The main competitive advantages of this methodological approach compared to other 3-D models proposed, is that the whole 3-D geometric information of the road construction is taken into account, and additionally, the available sight distance can be calculated for any potential trajectory followed by a vehicle. In addition, the methodology allows for universal adjustment that is not constricted by regional idiosyncrasies (i.e., existing design guides and policies). Finally, the computational part of this methodology is attained by expressing the functions in code through the programming language offered by the software Mathematica, whereas the whole process is demonstrated as a case study. It is noted that all the algorithms and codes appear in a fully automatic manner and parametric form, allowing the user each time, to set the corresponding and required input values to the algorithm.