[gameprogrammer] Re: curves
- From: Robbert de Groot <zekaric@xxxxxxxx>
- To: gameprogrammer@xxxxxxxxxxxxx
- Date: Thu, 29 Jul 2004 12:51:05 -0400 (EDT)
No too difficult to augment the piecewise Catmull Rom to be 0-t over the
whole set of control points.
n = number of control points.
Every point x has a t value of x/(n - 1)
Then given a t for the whole line we can get the t' of the piece that it
falls in on. Finding that piece is a simple linear search or binary search.
Say if it falls between points a and b. The entire line t for a is "at" and
t for b is "bt". Then the piece wise t will be...
t' = (t - at) / (bt - at)
Now it's just the use of the piecewise catmull/bezier formula to get the
actual point.
One thing to note though is that speed along the curve will vary depending
on the control points and tangents defining the curve. I think you'll get
that with any spline based smoothing though.
> 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?
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