Re: [boost] Geometry and spatial indexes, my opinion

Subject: Re: [boost] Geometry and spatial indexes, my opinion
From: Johan Råde (rade_at_[hidden])
Date: 2008-10-09 12:49:45

> Isn't the cross product 3D-only?

The 3-dimensional cross product can be extended to n-dimensions.
The n-dimensional cross-product takes (n-1) n-vectors as arguments
and returns an n-vector.
If the argument vectors are linearly dependent, then the return vector is 0.
If the argument vectors are linearly independent,
then the return vector is the unique n-vector such that
1. it is perpendicular to all the argument vectors
2. its length is equal the (n-1)-dimensional volume
of the parallellepiped spanned by the argument vectors
3. the argument vectors and the return vector form a positively oriented system.

--Johan