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The parametric vector form of a B-spline curve was defined in the Practice Problems as x(t) = [(1 – 1)°Po+ (3t(1 – t) – 3t + 4)P| +(3t²(1 – t) + 3t + 1)p2 + t°p;] for 0

The parametric vector form of a B-spline curve was defined in the Practice Problems as x(t) = [(1 – 1)°Po+ (3t(1 – t) – 3t + 4)P| +(3t²(1 – t) + 3t + 1)p2 + t°p;] for 0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The parametric vector form of a B-spline curve was defined in the Practice Problems as x(t) = [(1 – 1)°Po+ (3t(1 – t) – 3t + 4)P| +(3t²(1 – t) + 3t + 1)p2 + t°p;] for 0 <t < 1, where Po, 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.
Transcribed Image Text:The parametric vector form of a B-spline curve was defined in the Practice Problems as x(t) = [(1 – 1)°Po+ (3t(1 – t) – 3t + 4)P| +(3t²(1 – t) + 3t + 1)p2 + t°p;] for 0 <t < 1, where Po, 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.
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