Matrix4x3

A 3x4 affine transform, row-major: three rows of four (_11 to _34), so there is no bottom row and the transform is a rotation or scale part in the left 3x3 and a translation in _14, _24, _34. Rows are Vector4, columns have three entries. Matrix4x3 * Vector4 gives a Vector3, and Matrix4x3 * Matrix4x3 composes two transforms.

m := Matrix4x3_Identity;
m._14 = 7;
assert(m * xyzw(1, 2, 3, 1) == xyz(8, 2, 3)); // w = 1 picks up the translation
assert(m * xyzw(1, 2, 3, 0) == xyz(1, 2, 3)); // w = 0 is a direction