The first two questions deal with Bézier curves.
1. In the diagram below, a Bézier curve is to be drawn from P1 to P4 using control points P2 and P3 which are both located at 0,8.
Use the cubic Bézier formula for the curve:
Q(t) = (1 - t)3 P1 + 3t(1 - t)2 P2 + 3t2(1 - t) P3 + t3 P4
and apply it to the following figure. In particular, compute the x,y coordinates of the point on the curve at t = 1/2. By symmetry, this point should lie along the line from 0,8 to 8,0. Does it? Describe the convex hull of the four control points. Is the point you computed within this hull?
2. For the curve below, made up of two cubic Bézier curves, draw the control points P2, P3, P'2 and P'3, arranged in such a way that the curve directions at P1 and P'4 are correct and their is no discontinuity in the curve slopes at the meeting point P4, P'1.
