最好的四元数讲解视频

The comparison:

Eulers: simple conceptually but complex and confusing in practice.

Quaternions: conceptually confusing but shockingly simple and free to use in practice.

Content:

1) the overview of the benefits of quaternions;

2) a technical explanation of how quaternions represent rotations;

3) a simple intuitive mental model of quaternions.

Benefits of quaternions

What quaternions really shine is with the three axis rotations:

1) no gimbal lock or changing axes;

2) rotation interpolation is smooth and direct;

3) trivial to do calculations.

How do they actually work

Show quaternions work in 2d rotations on one axis:

1）represent the orientations with the coordinate of a point on a circle;

2) double the angle.

How to extend to more axes:

1) Rotation on two axes with three numbers, the quaternion is a point on a 3d sphere;

2) Rotation on three axes with four numbers, the quaternion is a point on a 4d sphere.

Why double the angle:

1) represent the rotation clearly;

2) double cover.

The quaternion components are not exposed to the user:

1) the coordinates can be put in all kinds of illegal places;

2) spherical linear interpolation is a further restriction.