Anisotropic pair correlation function, direction vector formulation

Estimate the anisotropic pair correlation function (2d and 3d), as defined in Stoyan 1991, f. 5.2-5.3. This one doesn't use spherical coordinates but direction vectors.

Usage

pcf_directions(
  x,
  directions,
  h,
  f = 0.15,
  correction = "translation",
  n_dir,
  r
)

Arguments

x

pp, list with $x~coordinates $bbox~bounding box

directions

Matrix of direction vectors

h

widths of epanechnicov kernels, vector of two values, for ranges and angles.

f

If h not given, use h=f/lambda^(1/dim) for range and h=f*pi

correction

"none" or translation. Translation only for rectangle box.

n_dir

Direction vector grid resolution (if units not given). See Details.

r

In case directions not given, use these lengths for generated directions.

Details

For example, in 2D the polar vector (r, theta) is now a vector (r*cos(theta), r*sin(theta)).

For 2d, we use a regular grid of n_dir steps on [0,pi], leaving out pi due to antipode-symmetry to 0. n_dir=7 is the default.

For 3d we use a triangular grid on the expanding sphere. This is generated by subdiving a regular icosahedron n_dir times. n_dir=2 is the default.