Spherical Mapping math HELP!


I’ll try posting this one here, as nobody replied on the beginners forum.

In short, I need to mimic OpenGL’s spherical mapping in a vertex program, but I’m stuck with the math. The documentation says the reflection vector is not using the standard reflection formula, instead f is computed as:

f = u - 2n’n’T u

where u is the vector to position in eye-space and n’ the normal in eye space. All this is ok, but what n’T means? What is the transpose of a vector and how is resolved in a multiplication?

I suppose the transpose of a column vector is the same, as a row vector.

If so, how do I multiply (in plain C) a column vector by a row vector (or viceversa) ?

Thanks in advance!

A standard matrix multiplication is row by column.
If you assume the vectors n’ and n’T as matrices n’ to be 3x1 and n’T to be 1x3 (row x colunm), then the multiplication n’n’T of these two gives a 3x3 matrix as result.
That’s called outer multiplication, whereas inner multiplication is the dot-product.

Though the OpenGL 2.0 spec actually says
r = u − 2 nf^T (nf u)
So it’s a dot product after all.

Check the OpenGL Programming Guide Appendix F, there is another example of this for the rotional matrix.

Thanks Relic. The notation bugged me, thinking it was not the standard reflection formula, that is using dot product and not the transpose of a vector. I got it working now!