Rational Cubic Bézier Curves

SubscriptBox[\(ω\), \(1, 2\)]

1.

υ

1.

control polygon (Bézier handles)

intersection

quadratic Bézier curve

This Demonstration shows a rational cubic Bézier curve, with green marks at two-thirds the distance of the points

P

0

and

P

3

to the intersection of

P

0

P

1

and

P

3

P

2

. When you drag the points

P

1

and

P

2

to the green marks and set the parameter

ω

1,2

to 1, the resulting curve is equivalent to a normal (

υ=1

) quadratic Bézier curve with points

P

0

,

C

, and

P

3

, where

C

is the red point of intersection. This is not the case if

ω

1,2

≠1

.