Graphics

Some notes or materials of key concepts and points in graphics learning.

Euler angle & Gimbal Lock

Euler angle

From Wikipedia, it has a gif which describes:

.

Euler angle intuitively describes a series of rotations to make a object rotated to expected angle in 3D dimensino. A gyroscope is a typical way using Euler angle keeps rotation axis constant:

Aircraft could be a most common example for a spatial rotation, which are described with Euler angles by three axes: Pitch, Roll, Yaw.

• The angles:

• The axes:

• The rotation:

Gimbal Lock

However, using three axes gimbal which describe Euler angle for rotation will reach a ambiguity when the gimbals (coordinate planes) are mounted together.

It is called Loss of a degree of freedom with Euler angles.

We can resolve it by quaternions in a real spatial rotation. But we can still use Euler angle to describe spatial rotation in a human readable way, when we are aware of the existence of the lock.