The paper presents a simple technique to assign parameter values to randomly measured points for the least squares fitting of B-spline surfaces. The parameterization is realized by projecting the measured points to a base surface. The parameters of the projected points are then used as the parameters of the measured points. The base surface is in fact a first approximation of the final fitted surface, and it can usually be created from some approximate boundary information in the form of either points or curves. A similar technique can also be used for B-spline curve fitting.