Transforms or back-transforms a set of coordinates according to
the geometric anisotropy parameters.
Usage
coords.aniso(coords, aniso.pars, reverse = FALSE)
Arguments
coords
an n x 2 matrix with the coordinates
to be transformed.
aniso.pars
a vector with two elements, psiA and
psiR, the anisotropy
angle and the anisotropy ratio, respectively. Notice that the
parameters must be provided in this order.
See section DETAILS below for more information on anisotropy parameters.
reverse
logical. Defaults to FALSE. If TRUE the reverse
transformation is performed.
Details
Geometric anisotropy is defined by two parameters:
Anisotropy angle
defined here as the azimuth angle of the
direction with greater spatial continuity, i.e. the angle between the
y-axis and the direction with the maximum range.
Anisotropy ratio
defined here as the ratio between the ranges
of the directions with greater and smaller continuity, i.e. the ratio
between maximum and minimum ranges. Therefore, its value is always
greater or equal to one.
If reverse = FALSE (the default) the
coordinates are transformed from the anisotropic space to the isotropic
space.
The transformation consists in multiplying the original
coordinates by a rotation matrix R
and a
shrinking matrix T, as follows:
X_m = X %*% R %*% T ,
where X_m is a matrix with the modified coordinates (isotropic
space) , X is a matrix with original coordinates (anisotropic
space), R rotates coordinates according to the anisotropy angle
psiA and T shrinks the coordinates according to
the anisotropy ratio psiR.
If reverse = TRUE, the back-transformation is performed, i.e.
transforming the coordinates from the isotropic space to the
anisotropic space by computing: