Math for Game Developers - Multiplying Quaternions

We learn how to combine two rotation quaternions to make one quaternion that does both rotations.

Derivation of the quaternion multiplication in this video can be found in the book "3D Math Primer For Graphics And Game Development" by Fletcher Dunn and Ian Parberry

The source code for this video will be combined with the source code for the next video.

[hdbx]

Not very many times I laugh during maths explainations but "...Well... I can't actually draw 4-dimensions in a 2-dimensional space" got me. Great video series (Y)

[khlorghaal]

This is the only easily understood explanation of the relation of complex numbers to rotation that I've found, and I've looked quite a bit.

[NeilRoy]

"hold your horses" - I laughed out loud at that point. ;)

[JaimeBeilis]

great video! You have good teaching skills

[vfxvision]

Thank you, The explanation was awesome

[arturoordonez-hernandez]

Nice! This was published on my birthday four years ago. How did u learn so much about Quaternions man? I haven't seen an explanation like this anywhere else online.

[MrUSFT]

These are frickin' excellent, man. Thank you!

[alexfish]

One way to think of it: "i" is "imaginary" because we have to imagine that a*a = -1, which doesn't happen in the real world (eg. 5*5=25 and -5*-5=25). Any number times itself will never result in a negative number, so let's just imagine it could.

[ww]

For q=q1×q2, how do I get q1 when I already know q and q2??

[arturoordonez-hernandez]

The problem presented with Angle-Axis is known as gimbal lock right? Which Quaternions solve.

[cgprojectsfx]

I'm trying to figure quarternions. If I have a Point Vector(4, 3, 1) with a Quaternion for example (.7, 1, 0.0). How do I go about it to look at something with a Point of (10, 5, 4) but making make sure the Quaternion Rotation angle is directed at the point?

[nz]

Awesome video man. Just one question, how would I rotate an object about a third axis. In this video you showed how to rotate an object about 2 axes but I am trying to rotate it about 3, x, y and z. How can I do that?

[timwlake]

Is it possible to multiply in another quaternion to have a third axis?

[its.levandowski]

According to Wikipedia the result of the multiplication between two quaternions should be: (w_r * w_s - v_r dot v_s, w_r * v_s + w_s * v_r + v_r cross v_s).

Why did you add the dot product between the two vector parts to the product between the two scalar parts instead of substractint it?

You can check that multipling a quaternion with its inverse and see that the multiplication won't give you the identity quaternion (1, 0, 0, 0).

[ty]

Not so helpful… for me anyway… well I Disagree with skipping the formalism… but thats on me i guess