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This report is concerned with incremental methods for computer graphics. The application of the incremental approach to some advanced problems in computer graphics is discussed and demonstrated. In Section II, the problem of fast curve generation and display is discussed. This section uses the mathematical approach to curves as a perspective projection of polynomial-curves in higher-dimensional spaces. Section III, also discusses a fast generation of curves, but using another mathematical approach, the linear-differences method, only two-dimensional curves are discussed. Section IV, shows how to make the Warnock algorithm, for hidden lines elimination, incremental. Section V, discusses the generation of half-tone images, in real time. Section VI, discusses an incremental method for finding the intersection of given line segments.