The parametric vector form of a B-spline curve was defined in the Practice Problems as

where p₀, p₁, p₂, and p₃ are the control points.

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.

Data From Exercise 1

Suppose a Bézier curve is translated to x(t) + b. That is, for 0 ≤ t ≤ 1, the new curve is

Show that this new curve is again a Bézier curve.

Transcribed Image Text:

x(t) = [(1-1)³ Po + (31 (1-1)² - 3t+4)P₁ +(3t²(1 t) + 3t+1)p2 +1³p3] for 0 ≤ t ≤ 1,