I didn't understand a single word but I feel much smarter having read this.
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If you pick random latitude and longitude values you won't get a uniform distribution of the points on Earth. You will statistically get more points towards the poles which you can see on the animation.
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Can someone explain why the first method is incorrect?
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Because latitude circles shrink towards the poles. Uniform selection of φ makes short & large circles equiprobable, so short circles “fill up” faster with random noise. To “fill up” all latitude circles at the same rate, one must select uniformly wrt perimeter, not φ.
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Put simply, the incorrect version: Gets a circle's circumference, then Rotates it 180° in 3D space to make the sphere. Here's the problem: When you rotate the circle, the part of the circle near to axis of rotation does not travel nearly as far as the rest of the circle. And so:
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If you pick 10 points near the axis of rotation, they will be much closer to each other than the rest of the surface (see the clusters around the two "poles"). The solution: Make the first step generate fewer points near the axis and more elsewhere.
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A simple and more intuitive approach is to generate a random X, Y, and Z, then scale your random vector to have length equal to the radius of the sphere.
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This is almost correct, but will concentrate points from the corners and edges of the cube more than the sides. You need to throw out any generated random points that lie outside of the sphere.
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This was correctly pointed out in the Star Trek episode featuring the crew’s landing on Talos 4. That Spock was something else.
Thanks. Twitter will use this to make your timeline better. UndoUndo
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That's a variable v not a √
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