[gameprogrammer] Re: curves
- From: Norbert Felde <fenor@xxxxxxxxxxxx>
- To: gameprogrammer@xxxxxxxxxxxxx
- Date: Thu, 29 Jul 2004 10:17:55 +0200
Hallo,
If I use Catmull Rom spline I need a t parameter going 0-1 between every
four controll points, so the whole curve is composed of more segments.
It is important that I should be able to go through the whole curve with
a paramter which is 0 at the start and 1 at the end of the curve
because I want to use equal length parts of the curve.
What I mean:
If I use the values 0, 0.25, 0.5, 0.75 and 1 of t than I get everytime
equal length lines between the different t values. ( 0 and 0.25, 0.25
and 0.5, ... )
Is there a method how I can get control points from Catmull Rom spline
for a NURBS?
Thanks,
Norbert
Robbert de Groot wrote:
> I thing you are probably looking for something like a Catmul Rom Spline.
> very similar to Bezier splines. Bezier splines use two control points
> between two points. Catmul Rom uses the points before and after the two
> points and uses the vectors these points make with the two points making the
> spline... Got that? :)
>
> [ASCII ART]
> . p1 .p3
>
> .p2 .p4
>
> Bezier:
>
> In bezier the spline will be made between p1 and p4 using p1->p2 as the
> start direction at p1 and the vector p3->p4 as the end direction at p4.
>
> Catmul Rom:
>
> For Catmul Rom the spline will be made between p2 and p3 using the vector
> p1->p3 for the start direction of the spline at p2 and p2->p4 for the end
> direction of the spline at p3.
>
>
> So if you have a series of points you can create a spline from only the
> control points with Catmul Rom and for the end points p1=p2 for the start
> and p3=p4 for the end.
>
> Bezier formula is:
> pointAtTime(t)=
> (1 - t) ^ 3 * p1 +
> 3 * (1 - t) ^ 2 * t * p2 +
> 3 * (1 - t) * t ^ 2 * p3 +
> t ^ 3 * p4
> where t goes from 0 to 1.
>
>>From the two vectors in the Catmul Rom case you can find the two control
> points for the bezier and use the formula.
>
> There is actually a formula for Catmul Rom but I don't have the reference
> with me handy. The above is just what I remember so you may have to hunt
> for more accuracy.
>
>
> --- Norbert Felde <fenor@xxxxxxxxxxxx> wrote: > Hallo!
>
>>This topic is not direct connected with game programming, but I hope you
>>could help me or write where should I search or query for a solution.
>>
>>The problem is:
>>I need a curve that should go through at least 7 controll points, it
>>must not swing if more points are given and I should be able to
>>parametrize it with only one independent parameter.
>>
>>curves I tried to use and why they do not answer the purpose:
>>
>>Lagrange interpolation: it swings if more than 6-7 points are given.
>>
>>Spline: it is composed of segments so there is no paramter that runs
>>over the entire curve.
>>
>>Nurbs: It dous not run through the controll points. I think with
>>different knot functions it should go throught the points pat than it
>>must be composed of segments.
>
>
>
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