Maths behind the lookat VOP

[TomRaynor]

I just want to clarify in my head the maths behind what is happening in this vop and was hoping someone could help spell it out.

 

So yeah I get that this vop is used to construct a 3x3 rotation matrix given two incoming vectors. My understanding of how this works generally is as described in this link:

 

http://gamedev.stackexchange.com/questions/20097/how-to-calculate-a-3x3-rotation-matrix-from-2-direction-vectors

 

So cross product the two vectors you have to get a third, and then cross this new orthogonal vector with the first vector to get a completely orthogonal frame.

Is this what the lookat vop is doing and if so are the "two location" and "up vector" the two input vectors? What is the from location all about?

 

I am trying to work out how I get a quaternion that represents the coordinate frame of my incoming N and up vectors.

 

I have attached a scene file showing an arrow being copied onto a point which has a z-positive normal and a y-positive up vector.

I am plugging the normal into the "to location" and the up vector into the "up vector". I am curious why my coordinate frame (and arrow) is flipping.

 

I'm sure it is really simple and obvious but any more detailed explanation into how this node works and why it is doing what it is doing would be great.

 

Also, any info on quaternions, what they are and how you use them would be great. I use them but feel I don't fully understand them.

P.S. The answer: "no one really understands them" I will not accept

 

Thanks.

matrixConstruction_v01.hip

[pezetko]

Some reading about quaternions:
https://developer.gnome.org/cogl/unstable/cogl-Quaternions-%28Rotations%29.html

Also see the links to external references on that page:
E.g. like this one is nice: http://www.isner.com/tutorials/quatSpells/quaternion_spells_12.htm

[TomRaynor]

Thanks Petr. Any idea how the look at or align VOPs work other than what is in the help?

[Guest tar]

Hey Tom - sounds like you're asking just for the maths side - have you looked into maths courses?

[TomRaynor]

I am familiar with the maths, manipulating vectors/matrices etc. I'm just trying to work out what the nodes are actually doing in more detail and how to use them.

[anim]

lookat() VEX function or VOP node uses from-to vector as negative X axis and up vector as positive Y plane 

so the flipping is obvious if you assumed that is uses positive Z

 

I think it's made that way to reflect Camera viewing direction (which is negative Z) as well as Object Look At parm orients negative Z in target direction

[rayman]

Math for lookat is really simple.

 

First vector : normalize( to location vector - from location vector )

Second : cross ( First vector , up vector )

Third : cross( First vector , Second vector )

 

They are probably not ordered this way but the idea is the same.\

 

For quaternions watch this :

http://www.youtube.com/playlist?list=PLW3Zl3wyJwWNWsJIPZrmY19urkYHXOH3N

Really nice explaination.

Edited March 31, 2014 by rayman

[TomRaynor]

Perfect, thanks Pavel. That is what I wanted to clarify. Thanks for the video links too. Great stuff!