We propose the "minvar" algorithm for computing continuous, continuously invertible, piecewise linear (PL) approximations of color space transformations that can serve as functional replacements wherever look-up tables are presently used. After motivating the importance of invertible approximants in color space management applications, we review the parameterization and computational implementation of PL functions as representing one useful instance of this notion. Finally, we describe the present version of the minvar algorithm and compare the approximations it yields with standard industrial practice — interpolation of look-up table data.