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Sub-division splines generate a number of new control points calculated fron the old control points. Both control polygons/grids define the same curve/surface. At each iteration the resulting new points are much greater in number than the old points and lie nearer to the actual curves. After a number of iterations, the generated points lie on the actual curve, very close to each other, and by displaying them on a computer screen the result is a smooth curve/surface. This paper describes a method, which is an extension to the Bezier sub-division method, where the resulting curve is an approximation curve which interpolates only the first and the last control points. The method is also derived for surfaces.

AN EXTENSION TO THE BEZIER SUB-DIVISION METHOD TO COMPLETELY APPROXIMATE CURVES AND SURFACES