Parametric Surface Rendering

Parametric surface [Fari02] is a surface defined by a tensor-product of parametric curves, which are represented by parametric equations. As such surface comes with a well defined mathematical definition, it becomes one of the most common geometric tools for computer-aided geometric design and object modeling aids for many computer graphics applications. Typical examples of such surface include Bézier surfaces [Fari02] and NURBS surfaces [Pieg97]. Unfortunately, since most existing graphics hardware only handles polygon, extra procedures must be carried out to convert a parametric surface into a polygon representation for rendering. This introduces a significant bottleneck to graphics applications, which involve parametric surfaces, to assure interactiveness in terms of rendering performance.