Let x(t) and y(t) be Bézier curves from Exercise 5, and suppose the combined curve has C2 continuity (which includes C1 continuity) at p3 . Set x"(1) = y"(0) and show that p5 is completely determined by p1 , p2 , and p3 . Thus, the points p0 ,,,,,,,,,,,p3 and the C 2 condition determine all but one of the control points for y(t).
Exercise 5
Let x (t) and y (t) be cubic Bézier curves with control points {p0, p1, p2, p3} and {p3 , p4 , p5 , p6}, respectively, so that x(t) and y(t) are joined at p3. The following questions refer to the curve consisting of x(t) followed by y(t) For simplicity, assume that the curve is in R2.
a. What condition on the control points will guarantee that the curve has C1 continuity at p3 ? Justify your answer.
b. What happens when x' (1) and y' (0) are both the zero vector?