[CST-2] NURBS circles...

[eycc2@cam.ac.uk]

> > > 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 ??
> >
> OK I think that follows from Vincent's answer - if we were taking the whole
> circle, P(t) would be for 0<=t<4, but since we're only doing a quarter
> circle, equivalent to just using [0 0 0 1 1 1], then t[max] = 1.

Vincent's right about the use of a quarter circle.  Here's what Neil Dodgson
wrote:

Equations 106,107, and 108 consider only one quarter of the curve definition.
Because we are using a quadratic B-spline and the knot value "1" is repeated,
the
section of the curve from t = 0 to t = 1 is completely defined by the
positions of the points P0, P1, and P2, which allows us to simplify the
mathematics considerably by considering only one quarter of the circle.
The other three quarters of the circle are identical in definition so,
once we have got the first quarter correct, we know what to do with the
other three quarters.


Neil
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