# 3D Rotation Maths Help (Global Rotation)

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I've been developing a 3D game engine for the purposes of learning and improving my coding skills. Now I've run into a big problem and I just can't seem to figure it out and after banging my head against a wall for countless hours I've decided to make my first post here on GDNet and humbly request some help.

Currently I can rotate my model around in local space no problems. However, I cannot for the life of me rotate it around a global axis.

Here is what I'm doing in short:

1. Create a Rotation matrix (R ) from an axis (Vector3) and an angle. (e.g. axis of 0.0f, 1.0f, 0.0f to rotate around the Y axis)

2. Then I multiply the model's matrix (M) by this rotation matrix (R). (i.e. M * R = new matrix after rotation)

Here's the code for the function. It is my own custom 4x4 Matrix class. I decided to make it instead of using GLM for learning sake.

template <typename user_t>
void Matx4<user_t>::TurnGlobal(Vec3<user_t>& axis, user_t angle)
{
Matx4<user_t> r;
Matx4<user_t>::Rotation(axis, angle, r); //Create the rotation matrix

(*this) *= r;  // Multiply the model matrix by the rotation matrix.
}

Now correct me if I'm wrong but I would have thought that doing this (i.e. M * R) would rotate M around the 'axis' in global space. However, it rotates it around local space instead. I'd first like to know if my assumption is correct or not. Should this methodology rotate around local or global space?

Secondly, if the above method is supposed to result in a local rotation, how do I go about making it global? I've tried so many things and nothing has been even close.

Any help will be greatly appreciated.

Edited by CaptKen

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It depends on the order of the mulitplications.

If you have M*R, you need to read it from right to left:  first rotate it by R (still in local space), then apply M (moving it into world space).

So, instead try R*M, that is, first transform it into world space, then rotate it around (0,0,0) by applying R.

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Friend you have got to be kidding me! Thank you.

I knew it would be something small like this but I just couldn't put my finger on it. Thank you so much. I just switched the two around and it works perfectly. Can't believe I didn't try this. lol

Much appreciated.

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The way I find clearest to think about this, adding nothing new here, is that a rotation is ALWAYS around the origin, whatever it happens to be when you do the rotation.

So to rotate around something other than the model local origin, you must first translate the model so your rotational centre is its new origin, then rotate, then you can translate the model back.

Hope this helps.

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