A mapping system for converting an input signal value to an output value wherein certain outputs are predetermined to be critical. An engine for converting input values to output values is associated with an input value transforming system wherein certain input values corresponding to the critical output values are transformed prior to input to the engine for adjusting the input value so that the engine generates a particularly desired output. The transforming comprises selecting a set of basis functions for effecting a warping of input values near the input value corresponding to the critical output value. The basis functions determine the extent and gradient of input value adjustment for nearby values to the critical value. The basis functions are included within an objective function defining the purpose of the system and the functions are solved to generate the desired adjusted input value. The system has particular applicability to color gamut mapping in a print system wherein output color needs to be accurately printed and colors nearby the critical color can be generated with minimal image artifacts.