A Generalization of Algebraic Surface Drawing

  • Jim Blinn

Published by Association for Computing Machinery, Inc.

The mathematical description of three-dimensional surfaces usually falls in one of two classifications; parametric and algebraic. The algebraic form is defined as all points which satisfy some equation F(x,y,z)=0. This form is ideally suited for image space shaded picture drawing, the pixel coordinates are substituted for x and y and the equation is solved for z. Algorithms for drawing such objects have been developed primarily for first and second order polynomial functions. This paper presents a new algorithm applicable to other functional forms, in particular to the summation of several gaussian density distributions. The algorithm was created to model electron density maps of molecular structures but can be used for other artistically interesting shapes.