Distort > Equations: How it works

[John Rostron]

I recently had difficulty in getting the Distort > Equations Filter to work as I thought it should, I was convinced that there was an error and posted a Bug report here. After comment from members @shojtsy and @walt.farrell and moderators @Andy Somerfieldand @Patrick Connor, I finally got it sorted. I thought that an item in the Tutorials might help for others coming to this problem anew.

Consider a simple pair of Equations:

x=x+y*0.2
y=y*0.7

My original thoughts were that these represented algebraic transformations, that the value of the pixel at position (x,y) would be moved to pixel position (x+y*0.2, y*0.7). Applying this to the image:

gives:

The bottom right corner of the image is transparent.

My expectation was that the height of the text would be reduced to 70%, but it is actually expanded to approximately 140% (1/0.7). I originally expected the slant to be anti-clockwise, but it was clockwise.

My original thoughts and expectations were wrong. What actually happens is quite different.

For any pixel at position (x,y), Affinity Photo will  find the pixel at (x+y*0.2, y*0.7) and use the value of the pixel value there to apply to the pixel at (x,y).

Following this logic, the results are consistent with (revised) expectations.

John