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Figure 2
An illustration of the Lambert projection of the top unit hemisphere. The indices S, L and E indicate, respectively, points on the sphere, in the Lambert projection and in the `standard' angular-equidistant projection for which the distance of the point from the centre is proportional to the spherical angle. (a) A three-dimensional illustration of some points on the unit sphere shown, in projection, in the other images. Points EP and LP illustrate the back projections onto the hemisphere of the point P in the plane with Rn = [{\sqrt 2}/2] and φ = π/3 shown in panel (d). (b) The Lambert projection conserves the distance from the north pole N. Red arrows indicate, for comparison, the angular-equidistant projection, with Rn = [n {\sqrt 2}/6], of the points with θ = nπ/12, n = 0, 1,…, 6. (c) The distance R from the centre for the angular-equidistant projection, in red, and for the Lambert projection, in blue, as a function of θ, quantifying the information in panel (b). (d) The angular-equidistant projection, in red, and the Lambert projection, in blue, of the arcs shown in panel (a).

Journal logoJOURNAL OF
APPLIED
CRYSTALLOGRAPHY
ISSN: 1600-5767
Volume 57| Part 3| June 2024| Pages 865-876
https://doi.org/10.1107/S1600576724002383
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