User:Romeolz/Isomorphic layouts: Difference between revisions

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<big>HERE IS '''EVERYTHING''' INTERESTING I HAVE FIGURED OUT ABOUT '''ISOMORPHIC LAYOUTS'''!!!</big>

This page is very much a work in progress, frankly it's a mess but I hope anyone reading this can benefit from it somehow!

Note: I am very much a math person and this is very theoretical for the time being. I mostly work in a Regular Temperament Theory (RTT) framework (sorry Domin).

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* ov ⇒ ov + nk*(x*oh + y*ov).

===== Warp (subtype of shearing) =====

===== Warp [WIP] (subtype of shearing, hexagon-exclusive) {come up with a better name for this} =====

~~asd~~

The warp operation preserves the look of the layout while stretching or compressing it along an axis (the oh axis in this case).

A single warp is a single shear operation combined with a <s>30° keyboard rotation</s>. apparently the rotation depends on the playing direction, more math that i just don't want to do right now

* Stretch:

** oh ⇒ oh - ov (ov ⇒ ov). Equivalent to shear, x=0, y=1, nk=1.

** <s>30° clockwise ↻</s>.

* Compress:

** oh ⇒ oh + ov (ov ⇒ ov). Equivalent to shear, x=0, y=1, nk=-1.

** <s>30° counterclockwise ↺</s>.

idk if this matters???: Keyboard rotation can be impractical, so there is also the double warp. It is two repeated single warps, but the same result can be derived with a different single shear operation and a <s>60° offset rotation</s>.

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 <big>HERE IS '''EVERYTHING''' INTERESTING I HAVE FIGURED OUT ABOUT '''ISOMORPHIC LAYOUTS'''!!!</big>
+This page is very much a work in progress, frankly it's a mess but I hope anyone reading this can benefit from it somehow!
 Note: I am very much a math person and this is very theoretical for the time being. I mostly work in a Regular Temperament Theory (RTT) framework (sorry Domin).
@@ Line 248: / Line 250: @@
 * o<sub>v</sub> ⇒ o<sub>v</sub> + n<sub>k</sub>*(x*o<sub>h</sub> + y*o<sub>v</sub>).
-===== Warp (subtype of shearing) =====
+===== Warp [WIP] (subtype of shearing, hexagon-exclusive) {come up with a better name for this} =====
-asd
+The warp operation preserves the look of the layout while stretching or compressing it along an axis (the o<sub>h</sub> axis in this case).
+A single warp is a single shear operation combined with a <s>30° keyboard rotation</s>. apparently the rotation depends on the playing direction, more math that i just don't want to do right now
+* Stretch:
+** o<sub>h</sub> ⇒ o<sub>h</sub> - o<sub>v</sub> (o<sub>v</sub> ⇒ o<sub>v</sub>). Equivalent to shear, x=0, y=1, n<sub>k</sub>=1.
+** <s>30° clockwise ↻</s>.
+* Compress:
+** o<sub>h</sub> ⇒ o<sub>h</sub> + o<sub>v</sub> (o<sub>v</sub> ⇒ o<sub>v</sub>). Equivalent to shear, x=0, y=1, n<sub>k</sub>=-1.
+** <s>30° counterclockwise ↺</s>.
+idk if this matters???: Keyboard rotation can be impractical, so there is also the double warp. It is two repeated single warps, but the same result can be derived with a different single shear operation and a <s>60° offset rotation</s>.