In Section 3.6 we found that the parametric form (x(t), y(t)) of the cubic Hermite polynomials through (x(0), y(0)) = (x₀, y₀) and (x(1), y(1)) = (x₁, y₁) with guide points (x₀+α₀, y₀+β₀) and (x₁−α₁, y₁−β₁), respectively, are given by x(t) = (2(x₀ − x₁) + (α₀ + α₁))t³ + (3(x₁ − x₀) − α₁ − 2α₀)t² + α₀t + x₀, And y(t) = (2(y₀ − y₁) + (β₀ + β₁))t³ + (3(y₁ − y₀) − β₁ − 2β₀)t² + β₀t + y₀.

The Bézier cubic polynomials have the form x(t) = (2(x₀ − x₁) + 3(α₀ + α₁))t³ + (3(x₁ − x₀) − 3(α₁ + 2α₀))t²,+3α₀t + x₀ and y(t) = (2(y₀ − y₁) + 3(β₀ + β₁))t³ + (3(y₁ − y₀) − 3(β₁ + 2β₀))t² + 3β₀t + y₀.

a. Show that the matrix

Transforms the Hermite polynomial coefficients into the Bézier polynomial coefficients

b. Determine a matrix B that transforms the Bézier polynomial coefficients into the Hermite polynomial coefficients.

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