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.

  ∴    V_y (0.5) = 3.5

∴          Midpoint         V (t = 0.5) = [3   3.5].