Random vectors with null sum
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Hello, I have a question for you. I have to initialize a number of 3D vectors, with fixed magnitude (intensity) equal to I, but the sum (in the geometrical sense) of vectors should be null. I prefer to work with angles (azimuth and elevation), but obviously a solution just considering the x-, y- and z-components of the vectors is fine, since thereafter I can make the transformation with cart2sph function.
Thanks a lot to all that could give me a support
Regards Matteo
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Walter Roberson
il 20 Giu 2012
Is the number of vectors to use known, or should it keep generating until it finds a solution?
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the cyclist
il 20 Giu 2012
Even in just one dimension, it's a non-trivial problem to combine random numbers to have a fixed sum. (The question comes up with some frequency here.) The following doesn't do exactly what you want (I don't believe), but you might be able to bend it to your needs.
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Walter Roberson
il 20 Giu 2012
Usually the easiest thing to do is to reject those (x,y) pairs and generate more. (Some of those might have problems too, so put yourself in a loop until you get N valid (x,y) pairs, each time generating (N minus number you have so far) samples.)
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