This paper describes improvements developed for an existing algorithm that calculates sight distance profiles based on horizontal geometry. Exact expressions are developed for vector derivatives for plane curves including clothoid spirals. Coordinate and derivative vectors are developed for partial spirals that possess nonzero curvature at both ends, frequently used as transitions between circular curves of different radii. As with complete spirals, the coordinate vectors are approximate and the derivative vectors are exact. Finally, an exact method for measuring distance along an offset curve to a clothoid spiral is developed. Taken together with the results in a previous referenced paper, this represents a complete recipe for computing sight distance profiles along arbitrary horizontal alignments. A numerical example is included to illustrate the use of the algorithm.
Journal of Transportation Engineering 127(4), pp.283-288