One issue that relates to graphics quality is the rendering of trimmed surfaces. In one approach, trimmed Non-uniform Rational B-spline (NURB) surfaces are rendered with Adaptive Forward Differencing. See "Rendering Trimmed NURBS with Adaptive Forward Differencing," by Shantz and Chang, Computer Graphics, Vol. 22, No. 4, August 1988, pp 189-198. In this approach, adaptive forward differencing is extended to higher order, the basis matrix for each scan is computed, the shading approximation function for rational surfaces is calculated, and the NURB surfaces are trimmed and image mapped. Trimming is accomplished by using AFD to scan convert the trimming curves in parameter space, producing the intersection points between the trim curves and an isoparametric curve along the surface. A winding rule is used to determine the regions bounded by the curve which are then rendered with AFD. In another approach, all trimmed surfaces are converted into individual Bezier patches with trimming regions defined by closed loops of Bezier or piecewise linear curves. Step sizes are calculated in parameter space for each curve and surface which guarantee the size of facets in screen space will not exceed a user specified tolerance. All points on the trimming curves where the tangents are parallel to the u or v axes are discovered, here, the local minima and maxima. Using the extremes, the trimming region of the patch is divided into u,v-monotone regions. Each region is defined by a closes loop of curves. Using the calculated step sizes, each u,v-monotone region is uniformly tessellated into a grid of rectangles connected by triangles to points evaluated along the curves. The polygons defined in u,v parameter space are transformed into facets in object space by evaluating their vertices with the surface factions. Surface normals are also calculated. Each facet is transformed to screen space, clipped, lighted, smooth shaded and z-buffered using 3D graphics hardware. See "Real-Time Rendering of Trimmed Surfaces," by Rockwood, Heaton, and Davis, Computer Graphics, Vol. 23, No. 3, July 1989, pp 107-116.
