Matrix Structure for screen rotation

Question

I can set my screen rotation to inverted with:

xrandr -o inverted
xinput set-prop 'ELAN Touchscreen' 'Coordinate Transformation Matrix' -1 0 1 0 -1 1 0 0 1

and back to normal with:

xrandr -o normal
xinput set-prop 'ELAN Touchscreen' 'Coordinate Transformation Matrix' 1 0 0 0 1 0 0 0 1

I found a HowTo here: https://wiki.ubuntu.com/X/InputCoordinateTransformation
So I guess for (90° to the right) it will be:

# ⎡ 0 -1 1 ⎤
# ⎜ 1  0 0 ⎥
# ⎣ 0  0 1 ⎦
right='0 -1 1 1 0 0 0 0 1'

But What is the right 'Coordinate Transformation Matrix' to the left?

Solution

Judging from the question it is a standard coordinate transform matrix.

So:

⎡x_out⎤   ⎡ a b c ⎤   ⎡ x_in ⎤
⎜y_out⎥ = ⎜ d e f ⎥ * ⎜ y_in ⎥
⎣z_out⎦   ⎣ 0 0 1 ⎦   ⎣ z_in ⎦

with z_out = z_in = 1.

I.e.

x_out = a * x_in + b * y_in + c
y_out = d * x_in + e * y_in + f

The example matrix you gave for right rotation

⎡ 0 -1 1 ⎤
⎜ 1  0 0 ⎥
⎣ 0  0 1 ⎦

thus means

x_out = 1 - y_in
y_out = x_in

for rotating left it would be the other way around i.e.:

x_out = y_in
y_out = 1 - x_in

giving the matrix

⎡  0 1 0 ⎤
⎜ -1 0 1 ⎥
⎣  0 0 1 ⎦

Comments

[Johan E]

Wouldn't it be [[0 1 0] [-1 0 1] [0 0 1]]. I.e. x and y are still swapped but it changes which of them that is inverted. The inverted coordinate has -1 in the upper-left 2x2 and 1 to the right, while the non-inverted coordinate have 1 in the upper-left 2x2 and 0 to the right.

[rubo77]

Note: by now the wiki page also includes the answer to the left matrix