Monotonicity preserving representations of curves and surfaces

Abstract

In this paper we revisit the problem of monotonicity preservation of curves and surfaces and we provide some new proofs and open problems. In particular, we prove a new formula for the derivation of rational Bézier curves. We also deal with the rational monotonicity preservation of rational Bézier surfaces and a related conjecture is presented.

Keywords

• monotonicity preservation
• axial monotonicity
• rational surfaces
• rational bilinear patch
• shape parameter
• shape preservation
• 65d17
• 68u07