[CST-2] NURBS circles...

[Vincent Wu]

I haven't actually done it... but since it says "we take one quarter of the
NURBS curve definition", I guess the knot vector should be [0 0 0 1 1 1] for
the quarter circle as there are 3 points and order 3.  Maybe that'll work...

----- Original Message -----
From: "Raymond Chan" <rwlc3@cam.ac.uk>
To: <CST-2@srcf.ucam.org>
Sent: Sunday, June 03, 2001 9:38 PM
Subject: [CST-2] NURBS circles...


> 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
>
>
>
>
>
>
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