mollweide {cooltools}

Mollweide projection

Description

Performs a Mollweide projection (also known as Babinet projection, homalographic projection, homolographic projection, and elliptical projection) of longitude and latitude coordinates. The most important feature of the Mollweide projection is that it preserves surface areas, which makes it a commonly used projection in geography, astronomy and cosmology. The total surface area of the standard projection is equal to the surface area of the unit sphere (4pi); and the shape of the fully projected sphere is an ellipse (with axes lengths 2*sqrt(2) and sqrt(2)).

Usage

mollweide(lon, lat, lon0 = 0, radius = 1, deg = FALSE)

Arguments

lon

n-vector of longitudes in radian (unless deg=TRUE)

lat

n-vector of latitudes in radian (unless deg=TRUE), must lie between -pi/2 and +pi/2

lon0

latitude of null meridian, which will be projected on to x=0

radius

radius of spherical projection, such that the surface area of the projection equals 4*pi*radius^2

deg

logical flag; if set to TRUE, the input arguments lon, lat, lon0 are assumed to be in degrees (otherwise in radians)

Value

Returns an n-by-2 matrix of 2D Cartesian coordinates x and y.

Author(s)

Danail Obreschkow

Examples

lon = runif(1e4,0,2*pi)
lat = asin(runif(1e4,-1,1)) # = uniform sampling of the sphere
plot(mollweide(lon,lat),xlim=c(-3,3),ylim=c(-1.5,1.5),pch=16,cex=0.5)
plotrix::draw.ellipse(0,0,2*sqrt(2),sqrt(2),border='orange',lwd=2)