Let be Bézier curves from Exercise 5, and suppose the

QUESTION:

Let x(t) and y(t) be Bézier curves from Exercise 5, and suppose the combined curve has \(C^2\) continuity (which includes \(C^1\) continuity) at \(\mathbf{p}_{3} . \text { Set } \mathbf{x}^{\prime \prime}(1)=\mathbf{y}^{\prime \prime}(0)\) and show that \(p_5\) is completely determined by \(p_1\), \(p_2\), and \(p_3\). Thus, the points \(\mathbf{p}_{0}, \ldots, \mathbf{p}_{3}\) and the \(C^2\) condition determine all but one of the control points for y(t).