On derivative bounds for the rational quadratic Bézier paths (Q1943000)

Let be \(V=\{(v_1,v_2,v_3) : v_i \in \mathbb{R}^d\}\) and \(\Omega=\{(w_0,w_2,w_3) : w_i\in \mathbb{R}^+\}\), where \(d \in \mathbb{N}\) and \(\mathbb{R}^+=\{x : x \in \mathbb{R}, ~x>0\}\). The rational quadratic Bézier path \(\sigma[v,w]\) with vertices \(v\in V\) and weights \(w \in W\) where \[ \sigma[v,w](t)= \frac{w_0(1-t)^2v_0+2w_1t(1-t)v_1+w_2t^2v_2}{w_0(1-t)^2+2w_1t(1-t)+w_2t^2}\qquad \text{for}\quad t\in[0,1], \] is investigated. New derivative bounds for the rational quadratic Bézier paths are obtained, both for particular weight vectors and for classes of equivalent parametrisations.