1. A device for mapping data from a source space to a target space, comprising: a memory that maintains a space transformation look-up table (LUT) that contains a plurality of locations, each of the plurality of locations includes, for each of a plurality of dimensions, a signal output value and information representing a derivative of a second-order or higher polynomial to be evaluated; and a component that performs actions, including: inputting first data defined according to a multi-dimensional source space; and generating second data defined according to a multi-dimensional target space, by applying information contained in the LUT to the first data.