Actually, you really want to compute a (hyper)plane (cross product) and then do dot products to partition the points. This is much faster (see my previous post on cross products as 'caches' of partially computed determinants.) Ditto for higher dimensions. At 01:33 PM 8/10/2013, Warren D Smith wrote:

For 2D, you need only to compute 3x3 determinant-signs in exact arithmetic (sign of area of a triangle), also expressible using 2x2 determinants.

In general a primitive to compute sign of (D+1)x(D+1) determinant will suffice.