1. In a computer graphics system having a CPU, a work station connected to said CPU for inputting graphics data to said system, means connected to said CPU for storing said data, and means connected to said CPU for outputting graphic illustrations on a video output device, an improved data processing pipeline for processing geometric figures which are composed of an array of both lines and curves, said CPU computing a plurality of vertices and at least one set of control points for each figure input at said work station such that each said line is defined by two end-point vertices and such that each curve of said figure is defined by a set of said control points, and said pipeline comprising: means for geometrically transforming any of said vertices or control points to a new position, said transforming means having an input port and an output port and the input port of said transforming means being connected to said means for storing said data; means for clipping any of said vertices or control points to a viewing frustum, said clipping means having an input port and an output port and the input port of said clipping means being connected to the output port of said transforming means; means for generating a series of data points which re-define each curve of said figure in terms of a series of straight line segments, said generating means having an input port and an output port and the input port of said generating means being connected to the output port of said clipping means whereby said straight line segments are generated only after the output from said clipping means of said clipped vertices and control points; and means for converting said lines and curves defining said figure to a format compatible for outputting said figure on said video output device, said converting means being connected to the output port of said generating means.