Fit a Bezier curve:
Fit a Bezier curve with the following control points : P0 (1, 1) P1 (3, 6) P2 (5, 7) and P3 (7, 4).
Determine points at t = 0.4 and 0.6.
Solution
We have four control points (n + 1)
∴ n = 3
∴ P (t ) = P0 (1 - t)3 + 3 P1 t (1 - t )2 + P2 t 2 (1 - t ) + P3 t 3
∴ x (t ) = 1(1 - t)3 + 3.3t (1 - t )2 + 3.5t 2 (1 - t ) + 7 t 3
= (1 - t)3 + 9 t (1 - t )2 + 15t 2 (1 - t ) + 7 t 3
∴ y (t ) = 1 . (1 - t)3 + 3 × 6 × t (1 - t )2 + 3 × 7 × t 2 (1 - t ) + 4 t 3
= (1 - t)3 + 18t (1 - t )2 + 21t 2 (1 - t ) + 4 t 3
P (t) = [x (t) y (t)]
∴ P (0.4) = [x (0.4) y (0.4)] = [9.3216, 5.08]
P (0.6) = [x (0.6) y (0.6)] = [4.6, 5.736]