Nonnegativity preserving macro-element interpolation of scattered data

Nonnegative bivariate interpolants to scattered data are constructed using some C1 macro-element spline spaces. The methods are local and rely on adjusting gradients at the data points to insure nonnegativity of the spline when the original data is nonnegative. As part of the analysis, a new condition for the nonnegativity of the cubic Clough–Tocher macro-element is obtained. More general range-restricted interpolation is also considered.