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(picks up the chalk)

I believe fervently that, in the 2D image space, this rotation to grad is useful:

• $M = M$: (no rotation)
• $a = 0, 90, 180, 270, 360$ degrees, or $\left[ 0 , 360 \right]$ degress
  • 1. N = 2dcfft(M); The elements are cos and sin, recall that?
  • 2. O = e^-ia(M); Element by element component rotation, ok?
  • 3. P = 2dicfft(O); Image reformation.

(offers chalk, no takers)

Note for $a = 0$, or $360$ degrees, $P = M$ to computational accuracy. So, WTF happens in between? Well, it's all about pencil sketches and modelling for art classes. I do that. And in the studio, I hold still, shut TF up, and think about the brain dynamics.

In between:

At $a = 90$, $O = \left| \nabla \left( M \right) \right|$. The other angles are left as an exercise for the interested reader!

Cheers from Dana at Replikon Dot Net Mathcad 6.0 Plus!

(chalk returned)