Abstract: Systems and methods of rendering curves through iterative refinement are disclosed. One such method of rendering a curve from a polygonal control loop 0P comprises iteratively applying k subdivisions described by Js to a series of polygons starting with 0P, where each subdivision is applied to the previous polygon.

Abstract: Surface modeling systems and techniques are described which approximate Catmull-Clark subdivision surfaces. A quadrilateral mesh is analyzed by applying shape and tangent masks to faces on the quad-mesh. Through application of the shape masks, a shape patch is created which approximates the subdivision limit surface. This shape patch can be used for rendering surface shape. Through application of tangent masks, tangent patches are created which comprise tangent vectors which give rise to continuous normal vector fields, which can be used for shading of the surface.