Let x(t) be a cubic Bézier curve determined by points p0, p1 , p2 , and p3.
a. Compute the tangent vector x' (t). Determine how x' (0) and x' (1) are related to the control points, and give geometric descriptions of the directions of these tangent vectors. Is it possible to have x' (1) = 0?
b. Compute the second derivative x"(t) and determine how x"(0) and x"(1) are related to the control points. Draw a figure based on Fig. 10, and construct a line segment that points in the direction of x"(0).
Fig. 10
