Geographic correction is necessary for all objects of the
class Transition that are either:
(1) based on a grid in a geographic (lonlat) projection
and covering a large area;
(2) made with directions > 4.
The function will correct for map distortion, as well as for diagonal
connections between grid cells (which cover a longer distance than vertical
or horizontal connections).
When working with lonlat grids, users should also anticipate whether they
will use methods based on either least-cost or random walks, and set the
type argument accordingly. In the case of least-cost distances, the
correction is only done in East-West direction. In the case of random walks
there should be an additional correction which reduces the conductance in
North-South direction (type="r").
The correction is done by dividing conductance values by the inter-cell
distance. Distances are calculated as great-circle distances for lonlat
grids (see function [raster]{isLonLat}) and Euclidean distances for all other grids.
In the case of randomised shortest paths, the need for correction is
somewhat in between these two correction methods. We have not developed
an analytical solution for this problem yet. With very low values for theta,
you may choose the correction for random walks, and for high values the one for
least-cost paths. Users who want to work with intermediate values of theta are
encouraged to experiment with different solutions.
The values are scaled to get values near 1 if the argument scl is set to
TRUE. This is desirable for subsequent calculations involving random walk
calculations. Values are divided by the W-E inter-cell distance (at the
centre of the grid).