Matrices
The Identity Matrix:
Matrices are what make 3d applications tick. If we didn't have matrices, rotation and translation would be impossible. We would have to directly set each vertex in a scene by hand! That is a nasty idea for any programmer with 3d experience. A standard matrix in a 3d world is 4x4.
1 2 3 4 | [1, 0, 0, 0][0, 1, 0, 0][0, 0, 1, 0][0, 0, 0, 1] |
If you multiplied a point through the matrix above, it would be equivalent to multiplying it by one- no change would take place. That is called an Identity matrix. Naturally we want a bit more than that, so we also have the...
The Translation Matrix:
tx, ty and tz represent our translation values.
1 2 3 4 | [ 1, 0, 0, 0][ 0, 1, 0, 0][ 0, 0, 1, 0][tx, ty, tz, 1] |
The Rotation Matrix:
Rotation on X Axis.
1 2 3 4 | [ 1, 0, 0, 0][ 0, cos(xrot), -sin(xrot), 0][ 0, sin(xrot), cos(xrot), 0][ 0, 0, 0, 1] |
Rotation on Y Axis.
1 2 3 4 | [ cos(yrot), 0, sin(yrot), 0][ 0, 1, 0, 0][-sin(yrot), 0, cos(yrot), 0][ 0, 0, 0, 1] |
Rotation on Z Axis.
1 2 3 4 | [ cos(zrot), -sin(zrot), 0, 0][ sin(zrot), cos(zrot), 0, 0][ 0, 0, 1, 0][ 0, 0, 0, 1] |
The Scale Matrix:
sx, sy and sz represent our scale values.
1 2 3 4 | [ sx, 0, 0, 0][ 0, sy, 0, 0][ 0, 0, sz, 0][ 0, 0, 0, 1] |
You can combine these matrices by multiplying them together. Transforming a point through any of these matrices will have the desired result.
Notice that translation changes the axis for any other operation. If you translated -5, and rotated on the y axis, the center axis will be at 0, 0, -5.