Interpolation and Curve Fitting

Bezier Curves
• Another variant of the same game
• Instead of endpoints and tangents, four control
points
• points p 0
and p 3
are on the curve
• points p 1
and p 2
are off the curve
• P(0) = p 0
, P(1) = p 3
• P’(0) = 3(p 1
- p 0
), P’(1) = 3(p 3
- p 2
)
3
2
P(
u)
u
u
u
1
2
2
1
3
3
2
0
0
1
1
0 0
1
P
1(0)
00
1
P0
(1) 00
0
P'
3(0)
3
0
0
P
0'
(1) 0
3
p 0
p 1
p 2
p 3
0
p
1
p
0
p
3
p
Numerical Methods © Wen-Chieh Lin 16
0
1
2
3