# 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 (t) are the Bernstein polynomials and the control points. It is always possible to write the expression in a standard form such that ==1. From such a form it is easy to determine the type of the conic section: if >1, it is a hyperbola; if =1, it is a parabola; and if <1, it is an ellipse.

C(t)=(t)+(t)+(t)(t)+(t)+(t)

B

0,2

ω

0

P

0

B

1,2

ω

1

P

1

B

2,2

ω

2

P

2

B

0,2

ω

0

B

1,2

ω

1

B

2,2

ω

2

B

i,n

P

i

ω

0

ω

2

ω

1

ω

1

ω

1