[CST-2] Advanced Graphics

[H. Zheng]

> Can anyone explain why with B-spline curves (page 13 of SMEG):
> "P(t) is validly defined for t_min<t<t_max where t_min = t_k and t_max =
> t_(n+2)"?
> Why can't the curve be evaluated at t_min=t_1 for example, and what has
> n+2 got to do with anything?

All the weights need to add up to 1.  That's only the case in the region
t_k to t_(n+2).

In fact, that's why the open uniform B-spline is open uniform, i.e.
t_k=...=t_1 and t_(n+2)=...=t_(n+k+1), so the curve starts at the first
point and ends at exactly the last point.  (Note that k-1=(n+k+1)-(n+2),
and that's why n+2.)

Cheers,
Han