npoly: Natural polynomials
In MomX/Momocs2: Modern Morphometrics and Shape Manipulation

Description Usage Arguments Details Value Functions See Also Examples

Calculates natural polynomial coefficients using stats::lm

npoly(
  x,
  degree,
  raw,
  drop_coo,
  from_coo = coo,
  to_coe = {     {         coe     } },
  ...
)

npoly_i(x, nb_pts, from_coe, ...)

`x`	coo_single, coo_list or mom_tbl
`degree`	polynomial degree for the fit (`degree+1`) coefficients are returned, see Details)
`raw`	`logical` whether to return raw and full results
`drop_coo`	`logical` whether to drop coo column (default to TRUE)
`from_coo, to_coe`	column names
`...`	for generics. Useless here.
`nb_pts`	number of points to sample and on which to calculate polynomials
`from_coe`	column name for inverse method

Curves must be registered on a bookstein baseline, with the first coordinates on (-0.5, 0) and the last on (0.5, 0). Use coo_bookstein

A polynomial of degree n use this fit:

y = a_{0} + a_{1}x^1 + a_{...}x^{...} + a_{n}x^{n}

And thus returns n+1 coefficients. The +1 being $a_0$ ie the intercept.

In retired Momocs, baseline was free and not necessarily Bookstein. Not sure this was really helpful but I'm sure this overcomplicated coding. If your shapes are not registered on Bookstein coordinates, you will be messaged (not for coo_single though)

a list with components when applied on a single shape:

coeff the coefficients (including the intercept)
ortho whether orthogonal or natural polynomials were fitted
degree degree of the fit (could be retrieved through coeff though)
baseline1 the first baseline point (so far the first point)
baseline2 the second baseline point (so far the last point)
r2 the r2 from the fit
mod the raw lm model

npoly_i: inverse npoly method

Other polynomials: opoly()

Other morphometrics: dfourier(), efourier(), opoly()

o <- olea %>% pick(5) %>% coo_bookstein()
o %>% pile()
op <- o %>% npoly(degree=3)
op
op %>% class

op %>% npoly_i() %>% draw()

olea %>% dplyr::slice(1:3) %>%
  npoly(drop=FALSE) %>% npoly_i