Systolic Array for Bicubical Polynomial Evaluation in Computer Graphics

A class of systolic architectures designed to evaluate bicubical parametric polynomials for a set of fixed and uniformly spaced values of the two parameters is presented. The arrays fit very well into a more general context in which special units are designed to convert the description of an object given in terms of parametric surfaces into a representation which is more convenient for the rendering algorithm, for example, ray tracing and ray casting. It can be demonstrated that a surface can be represented by means of a set of `surface patches', each one defined by means of a given set of control vertices. Three bicubical polynomials (one for each spatial coordinate) define each surface patch. The proposed hardware solution does not require dividers, but only shifters. The evaluation process produces 81 results for each polynomial, since a matrix of 9×9 different pairs of values of the parameters (u,v) has to be considered