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Subject: Re: Point Interpolation




"Just d' FAQs" wrote in message
news:r2mn52lbvja7ptv5se9f9bvkk9pgqt285i@4ax.com...
> On Fri, 5 May 2006 15:00:43 +0100, "Des"
> wrote:
> >I want to fit a curve through an ordered set of 2D points subject to the
> >following :
> >
> >1. curve is defined solely by the points
> >2. curvature is minimised in a global sense
> >3. adding a new point (in sequence) which is on the existing curve
results
> >in the same curve
>
> Curvature minimization is difficult and expensive; polynomial curves,
> even rational polynomial curves (NURBS) will not suffice. But if you
> can settle for minimizing acceleration, which is similar, then try a
> natural spline fit.

Thanks a million.

I did try to implement Gerald Farin's C2 cubic B-Spline with minimum
curvature (see page 136 of CAGD). I don't get entirely satisfactory results
but that may be due to a coding error. I think that approach is actually
minimum acceleration as you say.

If you have a copy of PhotoShop, then have a look at the "Curves" tool. This
posseses all of the properties I'm looking for - in particular adding a new
point on the curve doesn't change the shape of the existing curve, plus the
curve is defined only by the sequence of points. Do you (or anyone else)
have any idea what technique is used for this curve?

Many Thanks
Des



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