1123: Sidetrip

Mathematically, an affine transformation translates image coordinates, (x, y), to new coordinates, (x', y'), as follows:

x' = m₁₁x + m₁₂y + m₁₃

y' = m₂₁x + m₂₂y + m₂₃

For a pure rotation by an angle, theta,

m₁₁ = cos(theta)

m₁₁ = - sin(theta)

m₂₁ = sin(theta)

m₂₂ = - cos(theta)

and m₁₃ = m₂₃ = 0.

For a pure translation by (x_delta, y_delta),

m₁₃ = x_delta
m₂₃ = y_delta.

Other combinations provide flips, changes of scale, and even shears.