Assignment #8

Instead of Wednesday, this assignment is due on Friday, May 30, because of the Monday holiday.

Office hours: No office hour Tuesday, May 27. Instead, I'll have an extra office hour on Thursday, May 29, 2:30-3:30.

To do but not hand in:

CC-1, CC-3, CC-5, Cc-6, CC-9.

To hand in:

BB-1, BB-2;

CC-7, CC-10, CC-12, CC-18;

DD-1, DD-3.

Problem BB-1. For the cyclic spline interpolation problem with data points $S _ 0 = (4,1)$, $S _ 1 = (1,4)$, $S _ 2 = (1,1)$ (so $n = 3$), calculate cyclic B-spline control points $B _ 0, B _ 1, B _ 2$ that give back the $S _ i$ and sketch the resulting closed curve. (To get the equations use the discussion from lecture or re-develop them using the same principles as for the relaxed spline curves. You may be able to solve the linear equations by inspection. Use a large enough scale to give a meaningful picture.)

Problem BB-2. In the text, p.  132, §9.3, write out a derivation of equation (9.2) but using the notation more familiar from class: The Bézer curves are $P(t)$ and $Q(t)$ with control points $P _ 0, P _ 1, P _ 2, P _ 3 = S$ and $Q _ 0 = S, Q _ 1, Q _ 2, Q _ 3$.