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Daniel Zacharias wrote on Mon, May 20, 2024 07:27 PM UTC in reply to Lev Grigoriev from 05:27 PM:

Diagonal analogue and rotary counterpart are slightly different things.

To me, it's not so important what you call it. I think it was clear that I meant what you call diagonal analogue. It does necessarily involve extending the distance as well as 45° rotation.

irrelevant rambling about rotation

But if we measure distance in elemental steps, then N moves 3 W steps, and C likewise moves 3 F steps.

The other way works by defining moves differently. Instead of measuring N's move as being 3 steps by the most basic step on the same grid, we can say it's 2 K steps (where both W and F = 1). That way a rotation either increases or decreases the actual distance of the move, while preserving the measured distance in K steps.

So it all depends on how distance is measured. I like to think of rotation as replacing all Ws with Fs; and the second relation as inversion, swapping Ws and Fs for each other, but they do both involve both rotation and absolute distance changes.

"Rotational counterparts" might feel less natural since they don't have the weird effect of increasing some distances while decreasing others. Imagine rotating FD and getting WA. The short move got shorter and the long one longer! A diagonal analogue preserves the shape of the move without distortion. It's also like a screw—you can twist it two different ways to get different results.

What matters here is that CA is closely related to ND.


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