# Conic Section as Bézier Curve

Conic Section as Bézier Curve

Any conic section can be represented as a rational Bézier curve of degree two defined by , where are the Bernstein polynomials and the control points. It is always possible to write the expression in a standard form such that . From such a form it is easy to determine the type of the conic section: if , it is a hyperbola; if , it is a parabola; and if , it is an ellipse.

C(t)=

B(t)ωP+B(t)ωP+B(t)ωP

0,2

0

0

1,2

1

1

2,2

2

2

B(t)ω+B(t)ω+B(t)ω

0,2

0

1,2

1

2,2

2

B(t)

i,n

P

i

ω=ω=1

0

2

ω>1

1

ω=1

1

ω<1

1