= Rational quadratic Bézier curve
{title2=$R(t)=\frac{(1-t)^2P_0+2wt(1-t)P_1+t^2P_2}{(1-t)^2+2wt(1-t)+t^2}$}
A weighted quadratic <Bézier curve> with positive middle weight $w$ retains endpoint <interpolation> and endpoint tangent directions while changing the bulge. For a <circular arc> of angle $\theta$ less than $180^\circ$, choose endpoints on the <circle>, their tangent intersection as the middle <control point>, and $w=\cos(\theta/2)$. Unlike an ordinary nonconstant polynomial <Bézier curve>, this rational representation can describe a <circular arc> exactly.
Back to article page
