Maths & numbers
3D Euler rotation workspace
Apply an explicit X–Y–Z rotation order and inspect the resulting matrix.
A clear answer. Here’s how.
Applies active right-handed rotations to a column vector in a fixed Cartesian frame: X first, then Y, then Z. The combined matrix is Rz·Ry·Rx, which differs from other Euler conventions or intrinsic-axis sequences. Angles are degrees. Exports the rotated vector and the three matrix rows. The origin is fixed; translation and camera/projection conventions are excluded.
See a worked example
Worked example
A fixed demonstration, separate from the values you enter above.
- Vector X
- 1
- Vector Y
- 0
- Vector Z
- 0
- X rotation (degrees)
- 0
- Y rotation (degrees)
- 0
- Z rotation (degrees)
- 90
Example result
| Section | X | Y | Z |
|---|---|---|---|
| Rotated vector | 0.0000000000000000612323399574 | 1 | 0 |
| Rotation row 1 | 0.0000000000000000612323399574 | -1 | 0 |
| Rotation row 2 | 1 | 0.0000000000000000612323399574 | 0 |
| Rotation row 3 | 0 | 0 | 1 |
Active right-handed rotation of column vectors: X rotation first, then Y, then Z, so R=Rz Ry Rx. Angles are degrees.