[CST-2] NURBS circles...

[Raymond Chan]

Help! This is probably an easy question / I'm being very stupid - but has
anyone actually managed to derive equation (106) on page 19 of SMEG (the
maths bit of the graphics notes)? It's supposed to be the first part of the
NURBs representation of a circle. I understand what happens from (106)
onwards, but I just can't get from the NURBs equations to (106)...

here's an outline of what i've tried so far, hope someone can spot some
obvious mistake somewhere...

knot given is [0,0,0,1,1,2,2,3,3,4,4,4]
want quadratic, so k=3

N[1,1] = 0
N[2,1] = 0
N[3,1] = 1, 0<=t<1; 0, otherwise
N[4,1] = 1, 1<=t<2; 0, otherwise

N[1,2] = 0
N[2,2] = 1-t, 0<=t<1; 0, otherwise
N[3,2] = t, 0<=t<1; (1-t), 1<=t<2; 0, otherwise

N[1,3] = (1-t)t, 0<=t<1; 0, otherwise
N[2,3] = 2(1-t)t, 0<=t<1; (1-t)^2, 1<=t<2; 0, otherwise

from eqn(106) and comparing with eqn (105)...
surely N[1,3] should be (1-t)^2?
although N[2,3] looks right: 2(1-t)t from t=0 to 1
And why is P(t) from t=0 to 1 when surely it's from
t[min] = t[k] = 0, to t[max] = t[n+2] = 4 ??

I'm confused :-(

presumably the full derivation is examinable?

Raymond