A method, apparatus and article of manufacture are provided for performing rasterization using alternating sense point traversal. Upon receipt of a primitive, i.e. a triangle, a plurality of points are positioned on or near the primitive. Such points define an enclosed convex region and may be located at corners of the convex region. In operation, the points and convex region are moved in an alternating manner for the purpose of identifying an area in the primitive for rendering pixels therein. In particular, the points are moved in a boustrophedonic manner.