chromatic aberration paper mistake?

When I looked at the physical approach of Nvidia’s paper, I was very confused about one part of the equation:

sqr( I - n²(1-(N.I)²) )

N and I are vectors.

How can you take the square root of a vector,
and how can you subtract a scalar from a vector?
AFAIK it is not possible.
Should there be a 1 instead of the first I ?


What paper? I don’t mind this out.

I mean this paper:

The equation for the refraction vector seems to be false (Page 12).

There was a slight error in the equation. If you take a look at this web page,

you’ll see the correct equation.

The I vector under the radical should have been a 1.