A B-spline is built out of B-spline segments, described in Exercise 2. Let p0 ,,,,,,,,,, p4 be control points. For 0 ≤ t ≤ 1, let x(t) and y(t) be determined by the geometry matrices [p0 p1 p2 p3] and [p1 p2 p3 p4], respectively. Notice how the two segments share three control points. The two segments do not overlap, however-they join at a common endpoint, close to p2
a. Show that the combined curve has G0 continuity-that is, x(1) = y(0).
b. Show that the curve has C1 continuity at the join point, x(1) That is, show that x'(1) = y'(0).
Exercise 2
The parametric vector form of a B-spline curve was defined in the Practice Problems as
a. Show that for 0 ≤ t ≤ 1, x(t) is in the convex hull of the control points.
b. Suppose that a B-spline curve x (t) is translated to x (t) + b (as in Exercise 1). Show that this new curve is again a B-spline