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tags: Math
NOTE
Quaternions. I see these in development and I really lack the background knowledge to understand them. This is compounded by the fact they are, by general accounts, extremely abstruse and difficult to conceptualize.
I know I will fail at understanding them because I do not have the time or motivation. However, I am still curious to touch this. In the text below there are lines of “Don’t try to understand” - which I find intriguing. What are the reasons behind these acceptances?
It is also intriguing that from my weak understanding, it is basically used in graphics computation (rotation/shaders) because even though it is difficult to human-parse, a computer can use them to perform easier calculations. It also seems something called gimbal lock can occur if using Eulerian angles, where continuous rotation of an object causes an abrupt jump in a paramter.
In computer graphics, we use transformation matrices to express a position in space (translation) as well as its orientation in space (rotation). Optionally, a single transformation matrix can also be used to express the scale or “shear” of an object. We can think of this transformation matrix as a “basis space” where if you multiply a vector or a point (or even another matrix) by a transformation matrix you “transform” that vector, point or matrix into the space represented by that matrix.
Complex numbers introduced imaginary numbers meant to solve equations such as
The imaginary number has the form
Don’t try to understand this term, as there’s no logical way reason why it exists. We just have to accept that i is just something that squares to -1
Gimbal Lock
Gimbal lock is the loss of one degree of freedom in a multi-dimensional mechanism at certain alignments of the axes. In a three-dimensional three-gimbal mechanism, gimbal lock occurs when the axes of two of the gimbals are driven into a parallel configuration, “locking” the system into rotation in a degenerate two-dimensional space.
The term gimbal-lock can be misleading in the sense that none of the individual gimbals are actually restrained. All three gimbals can still rotate freely about their respective axes of suspension. Nevertheless, because of the parallel orientation of two of the gimbals’ axes, there is no gimbal available to accommodate rotation about one axis, leaving the suspended object effectively locked (i.e. unable to rotate) around that axis.
Thank god for games, now I understand this.
thing of note to easily understand gimbal lock: imagine you are playing a first person shooter and you point your gun vertically at 90°: you are no longer able to point the gun left and right, moving the mouse sideways only rotates alongside the gun’s axis. You have two axes locked in the same attitude providing the same rotation.