[CST-2] Graphics, knot vectors

[Lucy Lian]

Can anyone tell me what do we do with the "division by zero"s when
finding knot vectors? cos I don't quite understand the whole topic.

E.g. if the knot vector is [0 0 0 1 1 1], and for (0 <= t < 1)
(using []s for subscripts below):

N [1,1] = 0
N [2,1] = 0
N [3,1] = 1
N [4,1] = 0
N [1,2] = 0

then (no.s appending t's are subscripts too)
N [2,2] = ((t - t1)/(t3-t2)) * N[2,1] + ((t4 - t)/(t3-t3)) * N[2,1]
        = 0 + (1 - t)/0
where 0 is generated from (t3 - t3).

Working backwards from results given in notes N [2, 2] should be (1-t), so
should we just pretend that the zero is not there, or have I done
something wrong and it shouldn't be there?

The rest of the basis functions I got for this example are
(again for (0 <= t < 1)):

N [3,2] = t
N [1,3] = (1-t)^2
N [2,3] = 2t(1-t)
N [3,3] = t^2

but I'm not sure if they're correct, so it'd be great if someone could
check it.

Many thanks,
Lucy