Question

Find the coefficients of a cubic Hermite curve with the given conditions:

P₀ = (0,1), P₁ = (5,1), P'₀ = (93.5, 0), P'₁ = (0, -10)

a) P₀ = (0,1), P₁ = (5,1), P'₀ = (93.5, 0), P'₁ = (0, -10)
b) P₀ = (0,1), P₁ = (5,1), P'₀ = (93.5, 0), P'₁ = (0, -10)
c) P₀ = (0,1), P₁ = (5,1), P'₀ = (93.5, 0), P'₁ = (0, -10)
d) P₀ = (0,1), P₁ = (5,1), P'₀ = (93.5, 0), P'₁ = (0, -10)

Answer 1

To find the coefficients of a cubic Hermite curve, we can use the formula H(t) = (2t³ - 3t² + 1)P₀ + (t³ - 2t² + t)P'₀ + (-2t³ + 3t²)P₁ + (t³ - t²)P'₁. Substituting the given values and expanding the equations, we find the coefficients of the cubic Hermite curve.

Step-by-step explanation:

To find the coefficients of a cubic Hermite curve, we can use the following formula:

H(t) = (2t³ - 3t² + 1)P₀ + (t³ - 2t² + t)P'₀ + (-2t³ + 3t²)P₁ + (t³ - t²)P'₁

Substituting the given values, we get:

H(t) = (2t³ - 3t² + 1)(0,1) + (t³ - 2t² + t)(93.5, 0) + (-2t³ + 3t²)(5,1) + (t³ - t²)(0, -10)

Expanding and simplifying the equations, we find the coefficients of the cubic Hermite curve to be:

a₀ = (2t³ - 3t² + 1) = 2t³ - 3t² + 1

a₁ = (t³ - 2t² + t) = t³ - 2t² + t

b₀ = (-2t³ + 3t²) = -2t³ + 3t²

b₁ = (t³ - t²) = t³ - t²