visibility of objects in multi-dimensional space based on a specific perspective

I'm working on a data mining algorithm that considers features in their n-dimensional feature-space and allows surrounding training examples to block the 'visibility' of other training examples effectively taking them out of the effective training set for this particular query.

I've been trying to find an efficient way to determine which points are 'visible' to the query. I though the realm of computer graphics might offer some insight but there is a lot of information to peruse and much of it either can't be开发者_运维技巧 generalized to multiple dimensions or is only efficient when the number of dimensions is low.

I was hoping I could get some pointers from those of you who are more intimately knowledgeable in the domain.

The solution I found is to convert the euclidean coordinates into 'hyper-spherical' coordinates. Its similar to the spherical coordinate system except you add an additional angle with a range [0, pi) for each additional dimension beyond three.

After that I can sort the list of points based on their distance from the origin and iterate through comparing each point in the list to the first item looking for angles that overlap. after each iteration you remove the first item in the list and any items that were discovered to have been blocked. then start over with the new first item (closest item).

Don't know if anyone will ever find this useful but I thought I should put the answer up anyways.