A method for rendering a shape partially defined by quadratic Bézier curves computes the winding number with respect to one or more closed contours to determine whether a sample position is colored. Numerical robustness is achieved by classifying the controls points of each Bézier curve in order to partition the set of all possible Bézier curves into eight equivalence classes that can each be processed in the same manner. A small table of binary values specifies whether the roots of a classified Bézier curve are eligible to modify the winding number at a particular pixel location.