Flip ARFaceAnchor from left-handed to right-handed coordinate system

Question

After some testings by printing faceAnchor.transform.columns.3, digging in SO: ARFaceAnchor have negative Z position? and Apple\'s documentation: ARFaceAnchor,

Answer 1

At first, let's see what a default matrix values are.

Identity matrix

Here's an Identity 4x4 matrix with default values.

If you need additional info on elements of 4x4 matrices read this post.

 // 0  1  2  3
 ┌              ┐
 |  1  0  0  0  |  x
 |  0  1  0  0  |  y
 |  0  0  1  0  |  z
 |  0  0  0  1  |
 └              ┘

Position Mirroring

To flip entity's Z axis and X axis, in order to reorient axis from Face tracking environment to World tracking environment, use the following form of 4x4 transform matrix.

 // 0  1  2  3
 ┌              ┐
 | -1  0  0  0  |  x
 |  0  1  0  0  |  y
 |  0  0 -1  0  |  z
 |  0  0  0  1  |
 └              ┘

Rotation Mirroring

In 4x4 transform matrices rotation is a combination of scale and skew. To choose a right rotation's direction, clockwise (CW) or counter-clockwise (CCW) use + or - for cos expressions.

Here's a positive Z rotation expression (CCW).

Positive +cos(a):

 ┌                    ┐
 | cos -sin   0    0  |
 | sin  cos   0    0  |
 |  0    0    1    0  |
 |  0    0    0    1  |
 └                    ┘

And here's a negative Z rotation expression (CW).

Negative -cos(a):

 ┌                    ┐
 |-cos -sin   0    0  |
 | sin -cos   0    0  |
 |  0    0    1    0  |
 |  0    0    0    1  |
 └                    ┘