3 papers
math.NA2026
On the First Derivative Bounds for Rational Bézier Curves
Mao Shi
In this paper we investigate sharp upper bounds for the first derivative of rational Bézier curves. A long-standing conjecture posited that the linear bound $\|\mathbf{R}'(t)\| \l…
math.NA2026
Counterexamples to a Conjecture on First Derivative Bounds of Rational Bézier Curves
Mao Shi
In this paper we present an explicit counterexample of degree , which shows that the conjecture proposed by Li et al. \cite{Li2013} regarding the first derivative bounds for r…
cs.GR2024
On the derivatives of rational Bézier curves
Mao Shi
By studying the existing higher order derivation formulas of rational Bézier curves, we find that they fail when the order of the derivative exceeds the degree of the curves. In t…