  Polynomial interpolation is an important component of many computational
problems. In several of these computational problems, failure to preserve
positivity when using polynomials to approximate or map data values between
meshes can lead to negative unphysical quantities. Currently, most
polynomial-based methods for enforcing positivity are based on splines and
polynomial rescaling. The spline-based approaches build interpolants that are
positive over the intervals in which they are defined and may require solving a
minimization problem and/or system of equations. The linear polynomial
rescaling methods allow for high-degree polynomials but enforce positivity only
at limited locations (e.g., quadrature nodes). This work introduces open-source
software (HiPPIS) for high-order data-bounded interpolation (DBI) and
positivity-preserving interpolation (PPI) that addresses the limitations of
both the spline and polynomial rescaling methods. HiPPIS is suitable for
approximating and mapping physical quantities such as mass, density, and
concentration between meshes while preserving positivity. This work provides
Fortran and Matlab implementations of the DBI and PPI methods, presents an
analysis of the mapping error in the context of PDEs, and uses several 1D and
2D numerical examples to demonstrate the benefits and limitations of HiPPIS.
