Cross Vector on Box

[Justin K]

Hey all, interesting little math dilemmna here.  The problem is refining cross product  alignment on a simple 6 primitive box (see attached).  

Basically here is where I am at.  Im doing some work on quaternion based rotation systems.   Got a neat rig in place for geometry with well designed uvs-- 6- stacked quaternions for 3 axis--pitch, roll, and yaw, using vectors @N, @up, and v@cross - respectively. 

I thought I had a really solid system in place, until I test it on.......a box.........   

 

The issue is the cross product itself.  The cross products are aligning themselves sequentially-- basically wrapping around the box (see scene visualizer: "cross").   I mean it makes sense, but for the purpose of this scene,  I need to have all of the cross products pointing

1) towards the y axis, and

2) away from the object itself, and I want to do it procedurally.  

Any trig solutions solutions to this?  

12517_matrix_upld.hipnc

[vtrvtr]

The makebasis vex function let's you put custom orientation http://www.sidefx.com/docs/houdini/vex/functions/makebasis