3D & rendering

Quaternions in game development

rotations that take the short way

Interactive example · scroll or point here to play

rotations that take the short way

Euler angles store a rotation as three turns around the X, Y and Z axes, and blending those three numbers one by one sends the object on a detour. A quaternion stores the same rotation as four numbers, and slerp blends two of them along the shortest arc at a steady speed. Both ships turn between the same two orientations, and the nose trails show a 371° tumble on the left against a clean 143° arc on the right.

prompt bit

Store rotations as quaternions, combine them by multiplication, interpolate with slerp and negate one of the two when their dot product is below 0 so it takes the short way, and convert to Euler angles only for display or editor input.

When to use it

Use quaternions for camera turns, skeletal animation, and blending 3D orientations. They represent orientation, while angular velocity describes how quickly that orientation changes.

Implementation example

Engine-neutral pseudocode. Adapt the functions and coordinate conventions to your engine.

a = normalize(startRotation)
b = normalize(targetRotation)
if dot(a, b) < 0: b = -b
rotation = slerp(a, b, clamp(elapsed / duration, 0, 1))

Common mistakes

Quaternion multiplication is order-dependent. Normalize after accumulated numerical drift, and do not interpret the four components as four independent angles.

When to use it

Implementation example

Common mistakes

Further reading

Related concepts