(Read part one and the intermezzo first)

Before getting into quaternion rotations, let’s look at axis-angle rotations.

They are like Euler rotations, but not only around the X-, Y- and Z-axis, but around any axis (think of the picture in part one).

In Blender, you get 4 fields: W (the angle of rotation), X, Y and Z (the vector around which you rotate).

Now try this: choose any vector you want, but set the angle to 179°. Keyframe that value and set the angle at -179 at frame 23 or so and keyframe that value as well. Play the animation and you will see a rotation of -358°. This might be what you want, but imagine that you want a character’s hand to rotate a few degrees and it does something like this…

So we need something ‘better’ to describe  3D rotations. This is where quaternions come in and save the day.

Imagine a ‘copy’ of the 3D space we know and put it perpendicular to our 3D space. Let’s call this an imaginary 3D world. As this is a ‘copy’, we can make a direct ‘connection’ between any point in our world and the imaginary one. We can take Suzanne and put her in the corresponding place and orientation in the imaginary space.

You can think of a quaternion rotation as an axis-angle rotation performed in the imaginary world (twice!).

Under the hood, Blender takes the axis of rotation, divides it by it’s length, puts it in the imaginary world, along with the object that needs to be rotated, rotates it twice (uses a ‘sandwich multiplication’ by the quaternion, similar to the complex multiplication in the intermezzo) the first multiplication creates a real component, meaning we are now in a 4 dimensional world, the second multiplication (by the conjugate of the quaternion) brings it back in the imaginary 3D world and then Blender puts the rotated object back in the real world.

Compared to axis-angle, where the angle is in the W field and the axis vector in the X, Y, Z fields,

a quaternion has the angle represented in all 4 fields.

Mathematically (this is not important for us):

If the vector for the axis of rotation is (x, y, z), then:

W = cos(angle/2)

X = x*sin(angle/2)

Y = y*sin(angle/2)

Z = z*sin(angle/2).

Due to some clever properties of the imaginary components in this 6 dimensional space, we can now easily perform different rotations after one another (it’s just ‘sandwich multiplications’) and smoothly interpolate between rotations.

Usually, you do not want to fiddle with the numbers in the quaternion directly. They are hard to get 'right'.

(A quaternion in Blender for a rotation should be of length 1)

You can fill in the fields in an axis-angle and then switch to quaternion, if you want.

(The term quaternions in the title is short for/should actually be quaternion rotations.)

I get a message some one commented on my submission but cant find out where to locate said comments. Also waiting on a grade, so that I may either progress or re sculpt. They eye lids were terrible.

I've put all of my objects into "collections" (either WOOD or METAL). Try as I might, I cannot get anything to appear. I know I'm going to look back on this and laugh, but in the meantime I'm wasting a ton of time right-clicking the collections and enabling stuff/disabling stuff. I realize this is all part of learning (in this case, what "not to do"), but hard knocks learning sucks. Alt/Ctrl/Shift H variations are also getting me nowhere.

The Old Dog has about chewed his bone into shreds....

HELP!!!!!

<<EDIT>>

Okay... I don't know what I did to bring it all back. I switched from 3-D view to the image editor and back to the 3-D view and suddenly the invisible planks were present again. I've never been happier (well, I could come up with happy moments, but you know what I mean). But that doesn't explain how or why it happened. ugggg...

(Read part one first)

Suppose we want to multiply  the real number a by, let’s say 9.

That’s easy, right? 9 * a = 9a. Done!

Now let’s try that again, this time using complex numbers (we just learned about them and are awestruck by what they can do and we want to use them all the time…).

( A complex number is a 2 dimensional number, with a ‘real’ part and an ‘imaginary’ part; notation: a+ bi, a and b are real numbers. I am not going into that, you can Google complex numbers, they are well explained.)

Let’s try this: multiply a by (0 + 9i). Result: (0 + 9ai).

Well, partly a success. The ‘magnitude’ of a is now correct, but the number completely disappeared from the real world; it rotated into the imaginary world. In order to get it back into reality, we will multiply the result by the so-called complex conjugate of (0 + 9i) (again, the name is the only difficult part): (0 – 9i).

Now we get 81 as a result (i * i = -1, so i * -i = 1). We’re back into the real world, but now we have multiplied by 9 twice! Luckily there is an easy solution for this, called the square root.

So instead of 9i, we will use the square root of 9 times i, so: 3i.

The total formula we get is: 9 * a = (0 + 3i) * a * (0 - 3i) = 9a.

Hurray!         

(The numbers in the picture are different for scale reasons, principle is the same)

Notice that both times we multiplied by a complex number, we rotated in the same direction!

Let me begin with saying that, contrary to what most people seem to believe: quaternions are not hard.

The most difficult part is their name!

Imagine Hamilton (the 'inventor' of quaternions) and Euler, standing at the Origin.

They are told to go to the Light.

"That's easy", says Euler,  walks the necessary distance along the X-axis, then along the Y-axis and finally the Z-axis.

Hamilton says: "Tricky, but I can do it:" Looks at the Light and walks straight towards it until he reaches it.

Observe that Euler actually performed three 'special-case' Hamilton Translations, one after the other!

If you now imagine rotating around those translation axes, you've learned about 90% of what the difference between Euler Rotations and Quaternion Rotations is. (Still the part with the six dimensions to explain, but that's not that hard either, believe me.)

Hello, I wonder if it's possible to set up some way so you would open FBX just by double-clicking it in windows and blender would load it. Similar to how it works with Modo.

Are the serach functions on cgcookie ruined? I have tried to use it but it doesnt give the results i specify, and it also resets before you have done the actual search.