Term for similarity transformation which is not a translation What's the best (i.e. most concise) term to refer to an orientation-preserving similarity transformation which is not a translation? Here are some descriptions I could think of, but all of them feel rather bulky. I hope they are as equivalent to one another as I think they are, and I hope there is something simpler equivalent to all of them.


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*a direct similarity transformation which is not a translation (by a non-zero displacement)

*a homothety (possibly with factor $1$) followed by rotation (with possibly zero angle)

*an orientation-preserving similarity with at least one fixed point

*a direct similitude with a well-defined similitude center, or the identity

*what $z\mapsto a(z-c)+c$ describes in the complex plane, for some fixed $a,c\in\mathbb C$ (with $a\neq 0$)


As a native German, I tend to think about this using the German term “Drehstreckung” which literally translates to “rotation-dilation”. I'm somewhat surprised by the difficulty I have in finding an exact English translation for this concept.

I think that what you're looking for is simply called "affinity".  
From Wikipedia:

Examples of affine transformations include translation, scaling, homothety, similarity transformation, reflection, rotation, shear mapping, and compositions of them in any combination and sequence.

