What is responsible for the graph "Rotation in Quaternions"?
Changing the value itself does not lead to anything.
But with a general change / rotation of the bone, the value also changes.
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1 answer
Quaternions are an alternative to rotation in the corners. In principle, the corners are not ideal, for example, because of Gimbal Lock , when the axis of freedom is added up while the axis rotates and the degree of freedom is lost. In principle, there is no ideal rotation system; therefore, there are alternatives, such as quaternions.
First of all, divide in your mind the Euler angles and quaternions, angles are measured in degrees and radians, quaternions are more like a 4-dimensional vector, and the W-component has the same meaning as the other three. X, Y, Z and W are equivalent.
This topic is best described by James Grime , if you understand English. If it is not entirely clear I will describe it.
Imagine a 3-dimensional vector. This is not a quaternion, however it looks like it: 
The angle that forms a vector with vertical and horizontal planes can be expressed through this vector. However, unlike the quaternion, it is impossible to express the rotation of the vector around its axis. In general, the comparison of the quaternion and the vector is incorrect from the point of view of mathematics, but we omit it and consider the second example, for example, the coordinates of the vector 0,0,1.
It is not difficult to guess that a vector with such coordinates looks vertically upwards. Now the vector is 0,0,2. How is it oriented? Absolutely the same. Yes, it is longer, but the turn is the same. Thus, no matter how you scale the vector, it will not rotate. Similarly, by changing the W-compound quaternion, you change its length, but not the rotation. We also note that the same will happen with quaternions 1,0,0,0; 0.1.0.0; 0,0,1,0 and 0,0,0,1, since X, Y, Z, W are equivalent.
This property is also true for quaternions. You increase one part of the complex number, it changes the “value”, but not the rotation.
You might think that quaternions contain too much information, maybe it is. But they are loved in programming for the fact that you can rotate an object to the desired angle, no matter how difficult it would be to deploy, simply by multiplying the quaternions against each other.
Comparing the animation of rotation through Euler and quaternion angles
Why, when you rotate an object, does W change?
Rotation in the quaternion system is performed by multiplying one quaternion by another. And any turn not equal to 90 degrees is always expressed by at least 2 components. Here you have the change of 2 parts at the same time.
See also:
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