A Generalization of Algebraic Surface Drawing

Abstract

The mathematical description of three-dimensional surfaces usually falls into one of two classifications:
\nparametric and implicit. An implicit surface is defined to be all points which satisfy some
\nequation F (x, y, z) = 0. This form is ideally suited for image space shaded picture drawing; the pixel
\ncoordinates are substituted for x and y, and the equation is solved for z. Algorithms for drawing such
\nobjects have been developed primarily for fLrst- and second-order polynomial functions, a subcategory
\nknown as algebraic surfaces. This paper presents a new algorithm applicable to other functional
\nforms, in particular to the summation of several Gaussian density distributions. The algorithm was
\ncreated to model electron density maps of molecular structures, but it can be used for other artistically
\ninteresting shapes.