Fast display of curves and surfaces with correct topology in all resolutions

We present an efficient method for displaying curves and surfaces defined by implicit equations in such a way that the topology (connection) of the displayed curve is correct in whatever resolution. This is a consequence of detecting all the critical points of the curve and recursively subdividing the display region. Critical points are detected by evaluating the intervals, mean-value forms, and Krawczyk forms of the functions involved. We apply our method to visualizing surfaces by drawing their occluding contours. © 2000 Scripta Technica, Electron Comm Jpn Pt 3, 84(3): 1–11, 2001