### rviz's visualization of rotational elements of a co-variance matrix difficult to interpret

Hello,

I have a problem in how to interpret `rviz`

's visualization of co-variance matrix in PoseWithCovariance.

Visualization of translational elements (row:0~2, column:0~2) of co-variance matrices seems quite fine (purple-ish elliptic ball).

However, `rviz`

's visualization of rotational elements of co-variance matrices (row:3~5, column:3~5)
appears weird to me.

I believe three yellowish elliptic plates correspond to the error magnitude of
orientation frame axes (x axis, y axis and z axis) caused by rotational error.

If so,

- yaw noise should cause errors in x axis to direction of y and y axis to direction of x : --> all ellipses appear good.
- pitch noise ==> z axis to direction of x and x axis to direction of z : --> ellipse for z-axis seems weird.
- roll noise ==> y axis to direction of z and z axis to direction of y : --> ellipse for y-axis seems weird.

I would be pleased if anyone knowledgeable in `rviz`

give me some explanation on this phenomenon.

[ Co-variance Matrices ]

| 0.25 0 0 0 0 0 |
cov[3][3] = | 0 0.25 0 0 0 0 |
| 0 0 0.25 0 0 0 |
| 0 0 0 1.25 0 0 | # variance of roll noise is larger
| 0 0 0 0 0.25 0 |
| 0 0 0 0 0 0.25 |
| 0.25 0 0 0 0 0 |
cov[4][4] = | 0 0.25 0 0 0 0 |
| 0 0 0.25 0 0 0 |
| 0 0 0 0.25 0 0 |
| 0 0 0 0 1.25 0 | # variance of pitch noise is larger
| 0 0 0 0 0 0.25 |
| 0.25 0 0 0 0 0 |
cov[5][5] = | 0 0.25 0 0 0 0 |
| 0 0 0.25 0 0 0 |
| 0 0 0 0.25 0 0 |
| 0 0 0 0 0.25 0 |
| 0 0 0 0 0 1.25 | # variance of yaw noise is larger

[ Visualization by `rviz`

]

[ System that I used ]

- rviz: version 1.13.5
- ROS: melodic
- OS: Ubuntu 18.04.3 LTS
- Hardware: Lenovo ThinkPad X250

Thanks.