Symmetric Invertible $B$ – $H$ Curves Using Piecewise Linear Rationals

This paper introduces a technique for the construction of two monotonically increasing, continuously differentiable piecewise linear rational functions of the same form on the B-H plane-one mapping H to B, and its (exact) inverse mapping B to H-from an input data set of B-H point-and-slope values. Both curves are symmetric in that they consist of the same number of segments, each segment being of the same form and having the same computational cost of evaluation. Two means of determining slope values are presented: first, by construction of a single, high-order rational curve approximating a B-H data set, and second by synthesis of slope values by interpolation of consecutive triplets of points in the B-H data set using a linear rational function.