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I've run into a scenario where I want to describe something that can be rotated, translated (moved around) and scaled. However, calling out all those words in sequence is just ugly.
Example, "The picture on the screen is rotatable, translatable and scalable", which means that the picture can be rotated, moved around and zoomed in and out.
Is there one word to describe these three properties?
"Transformable"
A transform describes an operation that includes adding and multiplying the coordinates of the image (which would move it and scale it), as well as mixing them in different proportions (needed to rotate it)
Tighter than "linear transform" or "affine transform" is similarity transform. Alas, it still includes reflections. But it is the smallest hypernym that includes all of the ones you want. Isometry covers rotation and translation. Dilation covers scaling. Similarity has additional meanings outside of geometry. One characteristic of your set of operations is that they will always preserve angles. However, that fails as a governing criteria because there are transforms that preserve angles which can not be produced using your three operations (conformal maps.)
see this Wikipedia for a heirarchy - https://en.wikipedia.org/wiki/Geometric_transformation
