Curve of degree n, determined by n+1 control points P0, ..., Pn, using the Bernstein polynomials Bn,i(x) and n+1 additional (positive) numbers w0, ..., wn, called weights.
The curve is defined by the equation: c(t) = (1/BSum(x))*(Bn,0(x)*w0*P0 + ...+Bn,i(x)*wi*Pi + ...+ Bn,n(x)*wn*Pn),
where the function BSum(x) = Bn,0(x)*w0 + ...+Bn,i(x)*wi + ...+ Bn,n(x)*wn.
c(t), for positive weights wi, is contained in the convex hull of the set of control points. Here the curve is constructed using a small script (EUC_Scripts\EUC_Curves\RationalBezier.txt). n is the degree of the Bezier curve coinciding with the degree of the Bernstein polynomials used. The parameter t varies in the interval [0,1]. The curve below has degree 5 and 6 control points that can be freely moved.
Rational Bezier curves of degree 2 can represent exactly arcs of conic sections. This is illustrated in the file ConicThroughBezierRational.html .
![[alogo]](alogo.png){kind=small}
Rational Bezier Curve ![[0_0]](RationalBezier_files/RationalBezier_0_0_0.png)
![[0_1]](RationalBezier_files/RationalBezier_0_0_1.png)
![[0_2]](RationalBezier_files/RationalBezier_0_0_2.png)
![[1_0]](RationalBezier_files/RationalBezier_0_1_0.png)
![[1_1]](RationalBezier_files/RationalBezier_0_1_1.png)
![[1_2]](RationalBezier_files/RationalBezier_0_1_2.png)
![[2_0]](RationalBezier_files/RationalBezier_0_2_0.png)
![[2_1]](RationalBezier_files/RationalBezier_0_2_1.png)
![[2_2]](RationalBezier_files/RationalBezier_0_2_2.png)