It takes some points from the cartesian coordinates and maps them onto the sphere. The inverse os the Lambert's equal area projection.
lambert.inv(z, mu)A matrix containing spherical data (unit vectors).
A two- column matrix containing the Lambert's equal rea projected data.
The mean direction of the data on the sphere.
Michail Tsagris.
R implementation and documentation: Michail Tsagris mtsagris@uoc.gr and Giorgos Athineou <gioathineou@gmail.com>.
The data are first mapped on the sphere with mean direction equal to the north pole. Then, they are rotated to have the given mean direction. It is the inverse of the Lambert's equal are projection.
Kent, John T. (1982). The Fisher-Bingham distribution on the sphere. Journal of the Royal Statistical Society. Series B (Methodological) 44(1):71--80.
lambert
m <- rnorm(3)
m <- m / sqrt( sum(m^2) )
x <- rvmf(20, m, 19)
mu <- vmf.mle(x)$mu
y <- lambert( euclid.inv(x) )
lambert.inv(y, mu)
euclid.inv(x)
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