Abstract: We propose a method for fitting a piecewise parametric curve to a sequence of digitized points such as those acquired from a computer mouse or digitizing pen. The fitting is done on-the-fly rather than after a complete sequence of points has been acquired, thereby providing high-quality parameterized curves for immediate display during drawing. The method is fast, accurate, and robust, handles complex input paths, maintains corners, and ensures at least G1 continuity at non-corner points. The method uses vector distance fields, which we describe here, to represent the intended input path of the digitized points in order to achieve its quality and performance. Detailed pseudocode is available online.