Abstract: A method and apparatus for rendering a trimmed NURBS surface representing a mapping from U and V parametric coordinates to X, Y and Z geometric coordinates and having a trimming region bound by a trim polyline. The UV parametric surface is divided into contiguous V and V intervals intersecting to form UV rectangles, the trim polyline intersecting a subset of the UV rectangles to divide each of the UV rectangles of the subset into at least one polygon lying within the region and at least one polygon lying outside of the trimming region. For each UV rectangle intersected by the trim polyline, the vertices of each polygon within the trimming region formed by the intersection of the trim polyline and the UV rectangle is determined, and vertex data for the vertices so determined is provided to a concave polygon processor to render the polygon.