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Intersection point between n-vector and n-sphere

  1. Dec 14, 2012 #1
    Hello,

    I'm trying to compute the intersection point between a n-dimensional vector and a n-sphere.
    Do you know how to perform this? is it the same than 2 and 3 dimensions?


    I can't really find much information about this topic.
    Thank you very much,
     
  2. jcsd
  3. Dec 14, 2012 #2

    lavinia

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    Gold Member

    what have you tried so far?
     
  4. Dec 14, 2012 #3
    The statement is quite ambiguous as in general a vector doesn't need to have a common point with a sphere. Even if it's centred at the sphere's origin, its magnitude might be less than the radius of the sphere. You need to attach your vector to some point for this question to have meaning! Maybe you mean the intersection between an n-sphere and the n-line whose direction is defined by an n-vector that originates from a certain point? If so, what is the centre of the sphere, and what is the vector origin point?
     
  5. Dec 14, 2012 #4
    Hello,

    Sorry, I did not explain very good.

    Suppose that we have one n-sphere. Inside it, we have a n-point (this point different of the origin, it is another point named H).

    So, I have to compute the intersection of the line (that goes from the origin of the n-sphere passing from H) with the n-sphere. do you understand? is it possible?

    Thank you in advance again,
    Best.
     
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