Question

\text { (a) Find a cubic Bézier curve } \mathbf{x}(t), \mathbf{x}:[0,1] \rightarrow \mathbf{R}^{2} \text { with } \mathbf{x}(0)=\left(\begin{array}{l}

0 \\

0

\end{array}\right) \quad \text { and } \quad \mathbf{x}(1)=\left(\begin{array}{l}

9 \\

0

\end{array}\right) \text { which intersects itself orthogonally at } x\left(\frac{1}{4}\right) \text { and } x\left(\frac{3}{4}\right) \text {. } \text { (b) Construct a non-trivial Bézier curve } \mathbf{x}(t), \mathbf{x}:[0,1] \rightarrow \mathbb{R}^{2} \text { of degree } 4 \text { with } \mathbf{b}_{2}=\mathbf{x}\left(\frac{1}{2}\right) \text {. }

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