Hmm, right i am a Mathematics student at uni for a few years now… so if i can help you… i must be really crap at applied math and pure math. rofl
Well so i am not totaly understanding what you mean.
I think before you start making it complicated with the whole 3D aspect of another dimension make it simple first then move on.
So what if we just take a 2d grid of x and y axis, and for me i think isnt it
> x








^
y
where the top left is coordinated (0,0);
So ok if we defined some sort of 2d shape to be a helicopter take a rectangle for sake of arguemnt, (i would be worried if helicopters were just a rectangle not even a platonic solid haha);
Anyways lets say we have our rectangle
1—2
 
 
3—4
say 1:(0,0) 2:(2,0) 3:(0,4) 4:(2,4)
lets say that its curently facing down.
so what would happen if we turned it 90 degrees or pi/2 rads clockwise
lets see
31
 
42
so where are the coordinates now
well 3 seems to stay the same 3:(0,4)
4:(0,6)
1:(4,4) 2:(4,6)
so you can see a rotation you can do reflections just think of where the coordinates will be.
So your talking about roating things in 3D space:
for me from what i have learned that i should remember all off… but i dont haha think of vectors i am not sure how good your math knowlegde will be now, but if it isnt up to scratch i really reccoment a book on vector algebra and dynamics of particles or somthing like newtonion mechanics something like that
but anyways you will be looking for things about dot products cross products etc.
Your wanting to rotate an object though 90 degress in the y axis with respect to some other axis, immedietly this sounds complicated.
if you dont want to start getting too deep into mathematics just break it down so take it from the xaxis and yaxis perspective to find where a certain few vertices will be then do the same idea with the zaxis and yaxis perspective, try to visualise it as much as you can keep drawing it on a piece of paper or better yet get a few small shapes like cubes and cirlces (ellipse’s) etc
if you want to get a quick answer you can pretend your cylinder is a vector and you want to find what will happen that vector.
Example:
Lets say your cyclinder is face upward
in the yaxis
^




lets remember what our coordinate system is like in 3D
y


 /z
 /
/
x
its hard to show in ASC2 haha
anyways so we have a cyclinder standing up right in the y axis
then if you wanted to find what the vector will be and its coordinates would be in another axis you can do the crossproduct with the cyclinder vector and another axis
look at this don’t start looking at the matrix’s at the bottom only make things more confusing its handy when you start to understand it all
hmm actualy i’ll finish this later i have work to do hahaha