The exact clear zone envelope for piecewise-linear alignment data

This paper demonstrates how to construct the boundary of the clear zone adjacent to a roadway alignment, based only on horizontal sight distance considerations, when the alignment data are piecewise-linear on a fine lattice. In this case, it is shown that the clear zone envelope is piecewise-quadratic, and an efficient algorithm is given for constructing the parameters of each of the pieces of this curve. Special algorithm considerations are included, such as how to deal with overlapping and underlapping quadratic segments, as well as an efficient sort algorithm provided to initialize problem data properly.