Computational Techniques for Parametric Curves and Surfaces

Parametric curves and surfaces have b e en with us for a long time, and their use for object mode ling in Computer Graphics (as opposed to designing in CAD a pplica tions ) is still growing. There is sometimes. however, a r elucta nce t o use them because i t seems that the added power they give is more than otIse t by the complexity of their formulations and their computat.ions. The purpose of this paper is to make cleare r their meanings and uses, and show how much t h ey have in common behind the diversity of their formulations. The motiva tions, properties and references for the Hermite, Coons, Bezier, B-spline and {1-spline curves or surface s are given. The computation and display methods common in a standard graphics system are discussed (computations of points. geome tric transformations, display algorithms). The examples and illustrations a r e given for the curves and surfaces in their cubic form. Graphic. Interface '82