Euler Angles

The big idea

A position tells you where something is. An angle tells you which way it is turned. Euler angles (say it "OY‑ler") describe a turn by breaking it into three simple spins, one around each axis, done in order.

Picture turning a toy airplane in your hands:

• Pitch — nose tips up or down. This is a spin around the side‑to‑side axis (X).
• Yaw — nose swings left or right. This is a spin around the up‑and‑down axis (Y).
• Roll — the plane tips onto one wing. This is a spin around the front‑to‑back axis (Z).

Any turn, no matter how twisty, can be written as some pitch, then some yaw, then some roll. Those three numbers are the Euler angles.

How Cattail.Nu SpaceCube shows them

On a cube window's live readout you will see an Euler row with three numbers, one for each axis (X, Y, Z), in degrees. A degree is the everyday unit for angles: a quarter turn is 90°, a half turn is 180°, a full turn is 360°.

• If all three read close to 0°, the cube is sitting square with that frame.
• A cube tipped forward will show a non‑zero X (pitch).
• A cube spun to face a new direction will show a non‑zero Y (yaw).

The TXT export gives Euler angles in both degrees and radians (radians are just another unit for angles — see Concept - Quaternions).

Why we like Euler angles

They are easy to read. "Tilted 15 degrees" makes instant sense. That is why the app shows them, even though it stores rotations as quaternions to keep the math clean.

The catch

Euler angles get confused in extreme poses. With the cube pitched almost straight up or down, yaw and roll can trade places and the numbers turn twitchy. That problem is called "gimbal lock," and it is why the app keeps the real rotation as a quaternion and only converts it for display.

Related reading: Concept - Quaternions, Concept - World Space.