ABSTRACT
One of the very often-used classes of curves and surfaces are Bezier and Hermite curves and surfaces. The term spline comes from an early way of producing a smooth curve coming through given points used by engineers. They used a thin metal or wood strips forcing them to come through given points. A strip can come at any angle through the point. It was later shown that the strip takes a form corresponding to minimum energy. One important feature of NURBS is that they are invariant with respect to affine and perspective transforms. One class of relatively easy and often-met surfaces is called surfaces of revolution. These surfaces are produced by rotating a curve around some line in 3D. One of the classical surface subdivision schemes is the Catmull-Clark algorithm. It is performed on arbitrary polygonal meshes refining them.
