The math used by the implementation of GLKMatrix4MakeLookAt() cannot produce a useful point of view that looks directly along the “up” vector. The limitation exists because when looking directly “up” or “down,” the math used by GLKMatrix4MakeLookAt() attempts to calculate the tangent of 90 degrees, which is mathematically undefined.

Quaternions take advantage of 4D space to represent 3D angles.

Gimbal lock is the loss of one degree of freedom in a three-dimensional, three-gimbal mechanism that occurs when the axes of two of the three gimbals are driven into a parallel configuration, “locking” the system into rotation in a degenerate two-dimensional space.

Gimbal with 3 axes of rotation. A set of three gimbals mounted together to allow three degrees of freedom: roll, pitch and yaw. When two gimbals rotate around the same axis, the system loses one degree of freedom.