1. A method for calibrating a touch system, comprising: defining a set of calibration targets that have associated display coordinates (X i , Y i ) that are in a display coordinate system; accepting touchscreen coordinates (x i , y i ) that have noise, the touchscreen coordinates (x i , y i ) each being associated with one of the calibration targets, the touchscreen coordinates being in a touchscreen coordinate system; and computing non-linear correction parameters for a given polynomial expansion up to an order N (N≧3) that includes a set of polynomial terms based on the touchscreen coordinates (x i , y i ) in terms of the display coordinates (X i , Y i ), the non-linear correction parameters defining a one-to-one correspondence between display coordinates (X,Y) and touchscreen coordinates (x,y) that is non-linear, the computing comprising producing the one-to-one correspondence by using a linear combination of the polynomial terms to provide polynomial terms within the set that satisfy Laplace's equation and dropping at least some or all correction parameters corresponding to some polynomial terms violating Laplace's equation such that an average magnitude of a Laplacian of at least one of x and y touchscreen coordinates with respect to the display coordinates is smaller than an average magnitude of a Laplacian of a one-to-one correspondence computed with a conventional general fit in the presence of the noise of the touchscreen coordinates (x i , y i ), the Laplacians of the x and y touchscreen coordinates being based on ∂ 2 x/∂X 2 +∂ 2 x/∂Y 2 and ∂ 2 y/∂X 2 +∂ 2 y/∂Y 2 , respectively.