How to rotate an object around an arbitrary axis in 3D in 3D space?

I want to be able to rotate a 3D shape drawn in AE (or imported work of converted to a form) on one of its edges. I think that it is easier to explain with animation then here is a simple example of file and the film forms two triangle turning in the 3D space, one after the other.

The first rotation is easy because I can move to the anchor of the object to align with the left end of the triangle which is also parallel to the y-axis, then just turn 180 ° on the axis y over a period of 9 frame.

Second rotation is necessary on an edge that is not parallel to the axis X, Y or Z. So that by turn 180 ° with the x axis and 60º through the z over a period of 9 frame, the effect of the rotation isn't the edge desired flipping the eye reached in the first animated film. In order to do this, I need to be a sort of hierarchy of the parent object where I can turn the triangle.

I feel that I arbitrarily turn the model of triangle (for example, the vector A) aligned on one axis X, Y or Z and then animate the transition turn over time around one of these axes and turn then any return by A' be ion the correct location for the rest of the objects. As how to rotate a matrix it translates the object to be located about origin, to turn it and translate then return to the initial position a rotation about the origin of the object is not the origin of the global space. Don't know how to do this in AE.

axis of proper rotation for the first triangle:

Screenshot 2016-05-25 13.42.33.png

double shafts for second necessary triangle due to the fixed orientation of the local object space (autonomy seems wrong):
Screenshot 2016-05-25 13.37.33.png

Here is a simple configuration that I hacked together in a few minutes:

http://www.Mylenium.de/_temp/Technique_Triangle_Fold_00.zip

It is not really more than meticulously dealing with NULL values and other things to the order of rotation of the control. Of course, this can become complicated after some time...

Mylenium

Tags: After Effects

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