Parametric surface evaluation method and apparatus for a computer

Abstract

A method and apparatus for evaluating and rendering parametric surfaces. The apparatus includes a system memory connected to a graphics control processor, which is connected to local memory, and then connected in a pipelined arrangement to a plurality of parallel floating point processors, another floating point processor, a clipping processor and a frame buffer. The method includes: reading data from system memory and storing said data in local memory and/or registers within the graphics control processor; defining a control point stack containing kv by Nu transformed control points; multiplying the control points by a corresponding weight; evaluating the v dependence of homogeneous coordinates (wx,wy,wz,w) for successive parameter points separated by a v parameter interval; simultaneously within each parallel floating point processor evaluating the b-spline functions for one component of the coordinate set (wx,wy,wz,w) at successive u parameter points to obtain a top and bottom u coordinate, a top and bottom u derivative, and a top and bottom v derivative; eliminating the weight from each said coordinate yielding the geometric coordinates, and using the corresponding u and v derivatives to determine the geometric u and v tangents for a top and bottom point of an associated u value and therefrom the normal vector; clipping the polygon to the current viewing boundaries; and producing the shaded images of the polygon.