>> >Fortunately, they are integers, but what's the "near coplanarity" issue

>> >with floats?

>> Suppose, for example, you have a quadrilateral in the xy-plane,

>> and you rotate it into another plane with a floating-point rotation

>> matrix. The four vertices are still coplanar, but roundoff in the

>> computations may result in a slightly nonzero tetrahedron volume.

>> So the check volume == 0.0 will return FALSE even though the points

>> are coplanar.

>Is that an imprecision problem within the Floating point unit?

There are several issues here, but it is not a failure of the fpu.

For example, suppose you rotate the point (2,0,0) 30 degrees about

the z-axis. It's new coordinates are (sqrt(3),1,0). sqrt(3) cannot

be represented exactly in floating-point, so your double representation

of this point is slightly wrong, by about 2^{-50}. Four coplanar

points, all slightly wrong, may not give an exact zero volume.