Construction of Common Surfaces

Abstract

Sections 2 through 5 of this chapter cover the NURBS representation of the four surface types: bilinear surfaces, general cylinders (extruded surfaces), ruled surfaces, and surfaces of revolution. As the reader surely realizes by now, these representations are not unique. Considerations such as parameterization, convex hull, continuity, software design, application area, data exchange, and even personal taste can influence the choice of representation method. Our presentation closely follows the constructions given by Piegl and Tiller [Pieg87a]. Section 6 uses nonuniform scaling to obtain additional surfaces such as the ellipsoid and elliptic paraboloid. Section 7 presents a method for constructing a three-sided patch on a sphere, whose boundary curves are circles whose radii are equal to the radius of the sphere. This patch is useful as a corner fillet surface.