Determine the midpoint of Hermite cubic curve :
Determine the midpoint of Hermite cubic curve described by
V0 (0) = [1, 1], V1 (1) = [6 5] V ′0 (0) = [0 4] and V ′1 (1) = [4 0].
Solution
V0 (0) = [x0 y0] ∴ x0 = 1 y0 = 1 likewise x′0 = 0 y′0 = 4
V1 (1) = [x1 y1] ∴ x1 = 6 y1 = 5 and x′1 = 4 y′1 = 0
The midpoint may be calculated by putting t = 0.5 in the above equations.
∴ Vy (0.5) = 3.5
∴ Midpoint V (t = 0.5) = [3 3.5].