437/537 Homework 6

3.1

3.1 [2 pts] Ex 1c with (0,-2) changed to (-1,2).

[2 pts] Also express your answer in the monomial basis (i.e. 
expand and collect terms in powers of x).

3.1 [2 pts] Ex 2c with (0,-2) changed to (-1,2).


[2 pts] Verify this is the same polynomial you got in 1c.

3.1 Ex 11 [2 pts]

3.2

3.2 Ex 2 [5 pts: see solutions for breakdown]

3.4

3.4 Ex 8a [4 pts]

[3 pts] Also plot the cubic spline and mark the knots.
Hint:
fplot(S1, [x1 x2])
hold on
fplot(S2, [x2 x3])
axis([x1 x3 0 6])
hold off 

3.5

3.5.X [4 pts] Find the best 4-piece Bezier approximation to a circle.
 
[2 pts] How non-circular is it?
Some of the candidates for the quarter-circle are shown below.