A computer readable medium has instructions to calibrate a touch system by detecting touch points on a touchscreen that are each associated with touchscreen coordinates in a touchscreen coordinate system. The instructions associated each of the touch points with known calibration targets, and each of the calibration targets has display coordinates in a display coordinate system that is associated with at least one of a display screen and an operating system. The instructions fit the display coordinates and the touchscreen coordinates non-linearly with respect to each other based on a generalized Laplace-constrained fit that is used to identify correction parameters used to map a user generated run-time touch point on the touchscreen to a display coordinate location on a display screen. The correction parameters represent non-linear corrections.