Show that for 0 = t = 1, x(t) is in the convex hull

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Reference no: EM131074848

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

Reference no: EM131074848

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