Rational quadratic Bézier curve ($R(t)=\frac{(1-t{)}^2{P}_0+2wt(1-t)P_1+t^2{P}_2}{(1-t{)}^2+2wt(1-t)+t^2}$)

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.