🔄 Quaternion Rotation — Gimbal Lock & SLERP

🔄 What It Demonstrates

Euler angles (yaw, pitch, roll) are intuitive but suffer from gimbal lock: when two rotation axes align (e.g. pitch = ±90°), one degree of freedom is lost and rotations become erratic. Quaternions — four-dimensional numbers q = w + xi + yj + zk discovered by Hamilton in 1843 — represent rotations without singularities. SLERP (Spherical Linear intERPolation) smoothly interpolates between two quaternion orientations along the shortest arc on the 4D hyper-sphere, producing constant-angular-velocity motion with no jitter.

How to Use

• Adjust Yaw / Pitch / Roll sliders to set the target orientation.
• Enable Force gimbal lock to set pitch = 90° and observe how the Euler side loses a rotation axis.
• Toggle SLERP interpolation to see smooth vs. snapping behaviour on the quaternion side.
• Auto-rotate applies a continuous rotation so you can compare paths.
• The left cube uses sequential Euler rotation matrices; the right uses the equivalent unit quaternion.

Did You Know?

William Rowan Hamilton carved the quaternion multiplication rules (i² = j² = k² = ijk = −1) into Brougham Bridge in Dublin on 16 October 1843. Quaternions are now essential in aerospace (spacecraft ADCS), robotics, and every 3D game engine — Unity, Unreal, and Godot all default to quaternion rotations internally. The Apollo guidance computer used a gimbal-based inertial measurement unit; near gimbal lock the astronauts had to reorient the spacecraft to avoid losing navigation.