[comp.graphics] Evaluating 2-D parametric equations efficiently

kensy@microsoft.UUCP (Ken Sykes) (12/09/89)

Is anyone aware of efficient (preferably integer) evaluation of parametric
equations of the form
     x(t) = at^3+bt^2+ct+d
     y(t) = et^3+ft^2+gt+h
from t = 0..1

The best technique I have seen thus far is forward differencing which
results in three adds per component per point.  It would be nice if
there was something on the same complexity level of, say, bresenham
conics.  This code would be used to render 2D bezier curves (the 
coefficients are computed during a preprocessing phase.)

Also related to this, does anyone have an implementation of 
    "Adaptive Forward Differencing for Rendering Curves and Surfaces"
    Sheue-Ling Lien, Michael Shantz and Vaughan Pratt
    Sun Microsystems, Inc.

that they would be willing to part with?  The implementation I have
doesn't seem to perform as well as the paper implies.

Any help is greatly appreciated.  If there is sufficient interest I
will post a summary of the responses.

Thanks!
  Ken Sykes