determine length of bivariate polynomial

I think this will do it:

sum(sqrt(diff(x.pred)^2 + diff(y.pred)^2))

Michael

On Tue, Nov 8, 2011 at 11:34 AM, Nicolas Schuck
<nico.schuck at googlemail.com> wrote:

Dear R-community,

I have a fitted bivariate polynomial, i.e:

fit = lm(cbind(x, y)~poly(t, 15))

and I would like to determine the length of the line in the interval t =
[a, b]. Obviously, I could use predict and go through all the points, i.e.

for (t in a:(b-1)) {
length = length + sqrt((x.pred[t] - x.pred[t+1])^2 + (y.pred[t] -
y.pred[t+1])^2)
}

but that would take very long given the amount of data I have. Do you know
of any better solutions?

Many thanks!
Nicolas

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