A Generalization of Algebraic Surface Drawing

The technology of creating realistic and visually interesting images of three- dimensional shapes is advancing on many fronts. One such front is the develop- ment of algorithms for drawing curved surfaces directly from their mathematical definitions rather than by dividing them into large numbers of polygons. Two classes of surfaces which have received attention are the quadric and the bivariate parametric surfaces. Bivariate parametric surfaces are generated by three func- tions of two variables (most popularly polynomials), as the variables take on different values. Algorithms dealing with such surfaces are due to Catmull, Lane, Carpenter, Whitted and Blinn, and Clark.