This paper demonstrates how to approximate the boundary of the clear zone adjacent to a roadway alignment, based only on horizontal sight distance considerations. The alignment is divided into subproblems, and the clear zone boundary for each subproblem is approximated by a piecewise-linear space curve. The algorithms for this approximation are specifically designed to avoid numerical instability. Pseudocode versions of the algorithms are presented for the entire method. The errors in this approach are quite small compared to the expected errors generated while surveying and constructing roadways, and the error bound is shown to converge to zero uniformly as the parameter governing the resolution of the algorithm is made smaller.