A B-spline is built out of B-spline segments, described in Exercise 2. Let p 0,................, p 4

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A B-spline is built out of B-spline segments, described in Exercise 2. Let p0,................,pbe control points. For 0 ≤ t ≤ 1, let x(t) and y(t) be determined by the geometry matrices [pppp3] and [pppp4], 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 Ccontinuity at the join point, x(1). That is, show that x'(1) = y'(0).


Data From Exercise 2

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.


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Linear Algebra And Its Applications

ISBN: 9781292351216

6th Global Edition

Authors: David Lay, Steven Lay, Judi McDonald

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