opoly {Momocs}

Calculate orthogonal polynomial fits on open outlines

Description

Calculates orthogonal polynomial coefficients, through a linear model fit (see lm), from a matrix of (x; y) coordinates or a Opn object

Usage

opoly(x, ...)

## Default S3 method:
opoly(x, degree, ...)

## S3 method for class 'Opn'
opoly(
  x,
  degree,
  baseline1 = c(-0.5, 0),
  baseline2 = c(0.5, 0),
  nb.pts = 120,
  ...
)

## S3 method for class 'list'
opoly(x, ...)

Arguments

x

a matrix (or a list) of (x; y) coordinates

...

useless here

degree

polynomial degree for the fit (the Intercept is also returned)

baseline1

numeric the (x; y) coordinates of the first baseline by default (x= -0.5; y=0)

baseline2

numeric the (x; y) coordinates of the second baseline by default (x= 0.5; y=0)

nb.pts

number of points to sample and on which to calculate polynomials

Value

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

otherwise an OpnCoe object.

Note

Orthogonal polynomials are sometimes called Legendre's polynomials. They are preferred over natural polynomials since adding a degree do not change lower orders coefficients.

See Also

Other polynomials: npoly(), opoly_i()

Examples

data(olea)
o <- olea[1]
op <- opoly(o, degree=4)
op
# shape reconstruction
opi <- opoly_i(op)
coo_plot(o)
coo_draw(opi)
lines(opi, col='red')
# R2 for degree 1 to 10
r <- numeric()
for (i in 1:10) { r[i] <- opoly(o, degree=i)$r2 }
plot(2:10, r[2:10], type='b', pch=20, col='red', main='R2 / degree')