REMODELLING GIVEN BEZIER SPLINE CURVES AND SURFACES

Abstract

Rational Bézier splines offer many possibilities to control the shapes of curves and surfaces, but their relative complex equations lead at rather complicated formulas for derivatives and, consequently, smoothness conditions. In this paper we present a manner of partial or total remodelling given polynomial Bézier spline curve (part 2) and surface (part 4), preserving their class of continuity. The method consists in performing degree elevations that depend by real parameters. The curvatures of Bézier spline curve in the initial, final and joint points are also studied in part 3. The theory is illustred by some figures with initial (as witnesses) and remodeled spline curves and surfaces, respectively.