[R] Idea/package to "linearize a curve" along the diagonal?

[Jeff Newmiller]

Aren't you just reinventing the inverse of a function?
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Sent from my phone. Please excuse my brevity.

Emmanuel Levy <emmanuel.levy at gmail.com> wrote:

>Hi,
>
>I am trying to normalize some data. First I fitted a principal curve
>(using the LCPM package), but now I would like to apply a
>transformation so that the curve becomes a "straight diagonal line" on
>the plot.  The data used to fit the curve would then be normalized by
>applying the same transformation to it.
>
>A simple solution could be to apply translations only (e.g., as done
>after a fit using loess), but here rotations would have to be applied
>as well. One could visualize this as the "stretching of a curve",
>i.e., during such an "unfolding" process, both translations and
>rotations would need to be applied.
>
>Before I embark on this (which would require me remembering long
>forgotten geometry principles) I was wondering if you can think of
>packages or tricks that could make my life simpler?
>
>Thanks for any input,
>
>Emmanuel
>
>
>Below I provide an example - the black curve is to be "brought" along
>the diagonal, and all data points normal to a "small segment" (of the
>black curve) would undergo the same transformation as it - what
>"small" is remains to be defined though.
>
>    tmp=rnorm(2000)
>    X.1 = 5+tmp
>    Y.1 = 5+ (5*tmp+rnorm(2000))
>    tmp=rnorm(1000)
>    X.2 = 9+tmp
>    Y.2 = 40+ (1.5*tmp+rnorm(1000))
>    X.3 = 7+ 0.5*runif(500)
>    Y.3 = 15+20*runif(500)
>    X = c(X.1,X.2,X.3)
>    Y = c(Y.1,Y.2,Y.3)
>
>    lpc1 = lpc(cbind(X,Y), scaled=FALSE, h=c(1,1) )
>    plot(lpc1)
>
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