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Random Points on a Sphere

jasondavies.com · 316 words · saved by 1 readers

Suppose we want to generate uniformly distributed points on a sphere. We might start off by picking spherical coordinates (λ, φ) from two uniform distributions, λ ∈ [-180°, 180°) and φ ∈ [-90°, 90°).

Random Points on a Sphere Jason Davies → Maps Random Points on a Sphere Suppose we want to generate uniformly distributed points on a sphere. We might start off by picking spherical coordinates (λ, φ) from two uniform distributions, λ ∈ [-180°, 180°) and φ ∈ [-90°, 90°). However, we can quickly see that this will result in an uneven distribution, with the density increasing as we get closer to the poles. One way to explain this is to look at the how the area of a given “square” of width Δλ and height Δφ varies with φ. Try picking any square on the graticule (the spherical grid). See how the sq

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