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From: "John D'Errico" <woodchips@rochester.rr.com>
Newsgroups: comp.soft-sys.matlab
Subject: Re: distance between two points along a curve
Date: Sun, 9 May 2010 09:58:03 +0000 (UTC)
Organization: John D'Errico (1-3LEW5R)
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"Roger Stafford" <ellieandrogerxyzzy@mindspring.com.invalid> wrote in message <hs582h$o0b$1@fred.mathworks.com>...
> "John D'Errico" <woodchips@rochester.rr.com> wrote in message <hs54cv$3jk$1@fred.mathworks.com>...
> > ........
> >   dSdx = sqrt(1 + cos(x)^2)
> > ..........
> > But how do we find that point which lies at exactly
> > 25 units along that curve? Easiest is just to start the
> > solver at S(0) = -25. Then I'll just look for a zero
> > crossing. Save this function as an m-file on your
> > search path.
> > ........
> 
>   John, why wouldn't it be a lot easier to use 'ode45' to solve the differential equation
> 
>  dxds = 1/sqrt(1+cos(x)^2)
> 
> as I mentioned earlier?  Then you use s as the independent variable in 'ode45' from s = 0 to s = "desired distance", with x starting at the x value of point A.  That way you don't have to go to the trouble of searching for a "crossing event" along the way.
> 
> Roger Stafford

Yes. That is a better scheme yet.

John