an adaptive forward differencing apparatus , wherein , when rendering curves , calculated x , y values are increased or decreased in order to create values which correspond to the next pixel of the display crt , such that curves of substantially one pixel increments are continuously and uniformly generated . the apparatus also provides circuitry for generating coordinates of display elements which approximate an ideal vector and to define curves , vectors or objects within maximum and minimum coordinates of the crt display . the apparatus also provides efficient circuitry for computing the value of 1 / w of the homogenous coordinate w .