math - Generating random points on a surface of an n-dimensional torus -

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I want to generate random points on the surface of a n-dimensional torus. I have found the formula for generating points on the surface of: 

  x = (c + a * cos (v)) * cos (u) y = (c + a * cos (V)) * sin (u) z = one * sin (v)   
 u, v ??? [0, 2 * P); C, A & gt; 0.  
 My question is now: How to increase this formula to N dimensions Any help on this matter will be highly appreciated.  
  
 
 
 I think you can do it recursively by the complete physical basis of the place of your vector Start, and let the current location be original. In each step, choose a point in the plane spread by the first two coordinated vectors, i.e., w1 = cos (t) * v1 + sin (t) * v2 to another base vector, such as w2 = v3, w3 = v4, One ?? | | Also take a step from your current position in the direction of Wide 1, as well as radius R1 in front. When you have only one base vector remaining, then the current point, there is a point on the n-dimensional torus of the outermost recursive call.  
 Note that the above points can be used to choose randomly, it will not have to choose them equally, this will probably be a very difficult question, and you will definitely have to do it about mathematics Or perhaps before you get the right to the math before worrying about the implementation.

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