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Koroljov

Points on a sphere

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I wish to place N points on a sphere, so that the distance between a point and his "neighbours" is constant for all the points. If N=2, there should be 2 points: the intersection between the sphere and a line trough its center. If N=3, there should be 3 points on the sphere. These 3 points should form an equal-sided triangle. If N=4, there should be 4 points on the sphere. These points should form a tetraedron. Is there a way to calculate the points for any value of N? If yes, how? If no, why not? I need something like this for generating realistic trees.

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I think the answer is no.
A close approximation is a relaxation technique (place them at random and then move them as if they all repelled each other).
A good way to make trees is an L-system (google it) :o)

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