A Generalization of Algebraic Surface Drawing
J.F. Blinn · ACM Transactions on Graphics · 1982
The mathematical description of three-dimensional surfaces usually falls into one of two classifications: parametric and implicit. An implicit surface is defined to be 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 fLrst- and second-order polynomial functions, a subcategory known as algebraic surfaces. 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 it can be used for other artistically interesting shapes.