transformation 1 applied to original image
I created the published image above from a photograph by applying a simple plane-transformation. In this post I will try to explain how I did that.
The transformation that was applied was simple in the geometric sense. It wasn't simple to script. It comprises two orthogonal waves (sine curves), one running horizontally and the other running vertically. The plane-transformation that is created can be more clearly illustrated when it is applied to a regular checkerboard pattern.
Below is the image that is created from the checker board with the same transformation that was applied to the photograph. You can see that each square has remained complete but has either been squashed or stretched or both. The same local squashing and stretching has created the waves in the corn and the sky in the photograph.
|transformation 1 applied to checkerboard|
Although the published image was the result of a lot of fiddling with the details of the transformation (how big and how frequent are the waves, what happens at the edges), I wasn't totally satisfied with the large waves on the horizon (although I loved the clouds and the foreground). I was aiming for something more impressionist, where the landscape still looked realistic. So I altered the transformation to be the one shown below, where the waves near the horizon are more or less flat.
|transformation 2 applied to checkerboard|
|transformation 2 applied to original image|
I'm also pleased that I did the extra work involved in producing the second transformation, because I am now settled in my mind that the overly-wavy horizon in the published image is not a problem. It's a characteristic of the image that generates an important part of the impression that the observer sees.
Note: Actually it wasn't corn. It was an oil-seed crop, just after the flowers had died and just before it was harvested.