objects-and-simulations/affine.md

layout	title
math	Environment

Affine Transforms & Vector Math

Matrix multiplication
$ a, b, c], [d, e, f], [g, h, i x], [y], [z = ax + by + cz], [dx + ey + fz], [gx + hy + iz $

Translation
$ 1, 0, tx], [0, 1, ty], [0, 0, 1 x], [y], [1 = dot x], [dot y], [1 $

Scaling
$ sx, 0, 0], [0, sy, 0], [0, 0, 1 x], [y], [1 = dot x], [dot y], [1 $

Rotation theta
$ cos theta, -sin theta, 0], [sin theta, cos theta, 0], [0, 0, 1 x], [y], [1 = dot x], [dot y], [1 $

Shearing
$ 1, shx, 0], [shy, 1, 0], [0, 0, 1 x], [y], [1 = dot x], [dot y], [1 $

Affine Transform (Translation + Scaling + Rotation + Shearing)
$ sx * cos theta, -sin theta * shx, tx], [sin theta * shy, sy * cos theta, ty], [0, 0, 1 x], [y], [1 = dot x], [dot y], [1 $