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


i want able rotate 3d shape drawn in ae (or imported artwork ai converted shape) 1 of it's edges. think it's easiest explain animation here simple example file , movie of 2 triangle shapes rotating in 3d space 1 after other.

 

the first rotation easy can move object anchor align left edge of triangle parallel y axis, rotate 180º y-axis on 9 frame period.

 

the second rotation required edge neither parallel x, y or z axis. although rotating 180º through x-axis , 60º through z-axis on 9 frame period, effect of rotation not desired edge flipping achieved in first animation. in order either need kind of parent object hierarchy can rotate the triangle.

 

i feel need arbitrarily rotate triangle comp (say vector a) line x,y or z axis animate rotate transition on time around 1 of axes , rotate whole thing a' ion correct location rest of objects. how matrix rotate 1 translate object located on origin point, rotate , translate original position it's rotation relative object origin not world space origin. don't know how perform in ae.

 

 

proper rotation axis first triangle:

screenshot 2016-05-25 13.42.33.png

 

double rotation axes second triangle needed due fixed orientation of local object space (consonantly looks wrong):
screenshot 2016-05-25 13.37.33.png

project , art files (one ae file 1 ai fie may need relinked). triangles native ae shapes, ai file background triangles.

 

dropbox - green-triangles.zip



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