The numeric companion to tissot_map(): distortion sampled on a grid, so it
can be summarised, compared or mapped rather than eyeballed. Computed by
projecting a small circle at each grid point and measuring what happens to
it, which is the definition rather than an approximation of it.
Usage
projection_distortion(
projection = "equal_earth",
measure = c("areal", "angular", "max_scale"),
spacing = 10,
max_lat = 85
)Arguments
- projection
Projection to measure (see
projection_info()).- measure
"areal"(default; projected area divided by true ground area, so 1 is undistorted),"angular"(maximum angular deformation in degrees, 0 for a conformal projection) or"max_scale"(the larger principal scale factor).- spacing
Grid spacing in degrees (default
10).- max_lat
Absolute latitude limit (default
85).
Value
A tibble of lon, lat and distortion, with the area-weighted
mean and the range attached as the "countryatlas_distortion" attribute.
Reading the numbers
An equal-area projection has "areal" distortion of 1 everywhere – that is
what equal-area means, and it is worth checking rather than trusting.
A conformal projection has "angular" distortion of 0 everywhere and
unbounded areal distortion. A compromise projection is bad at both by a
little, everywhere, which is the trade it makes.
Distortion is measured against the WGS84 ellipsoid, the datum every CRS the
package builds is defined on. Equal Earth, Gall-Peters and the three Lambert
azimuthal projections have ellipsoidal forms and read exactly 1. PROJ
implements Mollweide and Eckert IV with their spherical formulas, so on this
datum they are equal-area only to within about 0.7% ("areal" between
0.993 and 1.007): a property of the maps drawn here, and the kind of thing
this check exists to show.
Examples
# \donttest{
if (requireNamespace("sf", quietly = TRUE)) {
d <- projection_distortion("mercator", measure = "areal")
attr(d, "countryatlas_distortion")
}
#> # A tibble: 1 × 5
#> projection measure mean min max
#> <chr> <chr> <dbl> <dbl> <dbl>
#> 1 mercator areal 4.37 1.01 131.
# }