User:Romeolz/Isomorphic layouts: Difference between revisions
operations, rotate, skew |
Shearing |
||
| Line 7: | Line 7: | ||
* Hobbled layouts | * Hobbled layouts | ||
* Coloring (albitonic and kite, edostep or albitonic gradient) | * Coloring (albitonic and kite, edostep or albitonic gradient) | ||
* scale (1 or 2 axis), shear, warp(the weird one) | * scale (1 or 2 axis), shear, warp(the weird one, apparently just a type of shear) | ||
* Bosanquet modifications | * Bosanquet modifications | ||
* HT extensions | * HT extensions | ||
| Line 137: | Line 137: | ||
Technically reflection is possible along any axis if you allow keyboard rotations, but that's not as useful and I can't be bothered to figure it out anyway.' | Technically reflection is possible along any axis if you allow keyboard rotations, but that's not as useful and I can't be bothered to figure it out anyway.' | ||
==== Shearing ( | ==== Shearing [WIP] (temperament preserving subtype of skew) ==== | ||
Shearing needs an axis and a number of keys. The axis is any direction that can be expressed as x*o<sub>h</sub> + y*o<sub>v</sub>. The number of keys (n<sub>k</sub>) can be any integer. | Shearing needs an axis and a number of keys. The axis is <s>any</s> direction that can be expressed as x*o<sub>h</sub> + y*o<sub>v</sub>. The number of keys (n<sub>k</sub>) can be any integer. | ||
Square grid: | Square grid: | ||
{| class="wikitable" | |||
|+temp: 12edo o<sub>h</sub>=1,o<sub>v</sub>=5, [gcd(x,y) and x*o<sub>h</sub>+y*o<sub>v</sub> mod 12] | |||
!4(4) | |||
!1(5) | |||
!2(6) | |||
!1(7) | |||
!4(8) | |||
!1(9) | |||
!2(10) | |||
!1(11) | |||
!4(0) | |||
|- | |||
!1(11) | |||
!3(0) | |||
!1(1) | |||
!1(2) | |||
!3(3) | |||
!1(4) | |||
!1(5) | |||
!3(6) | |||
!1(7) | |||
|- | |||
!2(6) | |||
!1(7) | |||
!2(8) | |||
!1(9) | |||
!2(10) | |||
!1(11) | |||
!2(0) | |||
!1(1) | |||
!2(2) | |||
|- | |||
!1(1) | |||
!1(2) | |||
!1(3) | |||
!1(4) | |||
!1(5) | |||
!1(6) | |||
!1(7) | |||
!1(8) | |||
!1(9) | |||
|- | |||
!4(8) | |||
!3(9) | |||
!2(10) | |||
!1(11) | |||
!0(0) | |||
!1(1) | |||
!2(2) | |||
!3(3) | |||
!4(4) | |||
|- | |||
!1(3) | |||
!1(4) | |||
!1(5) | |||
!1(6) | |||
!1(7) | |||
!1(8) | |||
!1(9) | |||
!1(10) | |||
!1(11) | |||
|- | |||
!6(10) | |||
!1(11) | |||
!2(0) | |||
!1(1) | |||
!2(2) | |||
!1(3) | |||
!2(4) | |||
!1(5) | |||
!2(6) | |||
|- | |||
!1(5) | |||
!3(6) | |||
!1(7) | |||
!1(8) | |||
!3(9) | |||
!1(10) | |||
!1(11) | |||
!3(0) | |||
!1(1) | |||
|- | |||
!4(0) | |||
!1(1) | |||
!2(2) | |||
!1(3) | |||
!4(4) | |||
!1(5) | |||
!2(6) | |||
!1(7) | |||
!4(8) | |||
|} | |||
'''<big>NOT ALL AXES WORK!!!</big>''' (for some reason, I'm still figuring it out) 12edo o<sub>h</sub>=1,o<sub>v</sub>=5, x=-1, y=2 doesn't work (requires 24edo) | |||
The cardinal directions and diagonals are guaranteed to work because the four keys next to the origin have 1 as the lead digit or gcd(x,y) going off infinitely along the diagonals and rows or columns. (?) | |||
* x=-1, 0 or 1 | |||
* y=-1, 0 or 1 | |||
* o<sub>h</sub> ⇒ o<sub>h</sub> - n<sub>k</sub>*(x*o<sub>h</sub> + y*o<sub>v</sub>). | * o<sub>h</sub> ⇒ o<sub>h</sub> - n<sub>k</sub>*(x*o<sub>h</sub> + y*o<sub>v</sub>). | ||
* o<sub>v</sub> ⇒ o<sub>v</sub> + n<sub>k</sub>*(x*o<sub>h</sub> + y*o<sub>v</sub>). | * o<sub>v</sub> ⇒ o<sub>v</sub> + n<sub>k</sub>*(x*o<sub>h</sub> + y*o<sub>v</sub>). | ||
Hexagonal layout: | Hexagonal layout: '''<u>(I wouldn't trust these formulas yet!!!)</u>''' | ||
* o<sub>h</sub> ⇒ o<sub>h</sub> - n<sub>k</sub>*(x*o<sub>h</sub> + y*o<sub>v</sub>).???????? | * o<sub>h</sub> ⇒ o<sub>h</sub> - n<sub>k</sub>*(x*o<sub>h</sub> + y*o<sub>v</sub>). ???????? | ||
* o<sub>v</sub> ⇒ o<sub>v</sub> + n<sub>k</sub>*(x*o<sub>h</sub> + y*o<sub>v</sub>). | * 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) ===== | |||
asd | |||