Abstract
NonUniform Rational B-Splines (NURBS) are the standard for describing and modeling curves and surfaces in computer-aided design and computer graphics. These are used to model everything from automobile bodies and ship hulls to animated characters in feature-length films. Curves and surfaces are mathematically represented explicitly, implicitly, or parametrically. This chapter describes parametric curve and surface representations. Although many surfaces can be represented analytically, there are also many surfaces for which analytical descriptions do not exist. Typical examples are automobile bodies, aircraft fuselages and wings, ship hulls, sculpture, bottles, and shoes. These surfaces are represented in a piecewise fashion that is similar to a patchwork quilt. The chapter discusses two kinds of continuity, or smoothness, associated with parametric curves and surfaces—geometric continuity and parametric continuity.
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