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# 2D vs 3D Camera transform matrix

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2 replies to this topic

### #1Believe82  Members

Posted 17 December 2013 - 02:58 PM

I was hoping someone could clear something up for me...

In 3D space, to obtain the camera view transform matrix, I believe it is scale * rotation * translation matrix.

However in 2D space (I've been working on a small project) I found it is actually the translation matrix * scale matrix, or the camera sometimes comes up with odd behavior.

After doing some searching online, I found for 3D camera problems the correct sequence was what I put above, same for 2D. I was wondering can someone offer a quick explanation as to why that is?

I'm just confused as to why you scale first then move the sprite for 3D, and move first then scale the model for 2D, since all 2D is missing is the Z axis.

Additional Info: I'm coding in MonoGame (XNA)

### #2haegarr  Members

Posted 17 December 2013 - 03:18 PM

There is no dependency on dimensionality with regard to the order of transformations.

In 3D space, to obtain the camera view transform matrix, I believe it is scale * rotation * translation matrix...

Such statements are meaningless as long as

(1) one tells whether column vectors (like e.g. typically in OpenGL) or else row vectors (like e.g. typically in D3D) is used, and

(2) one tells what exactly the "camera view transform" means, and

(3) one tells what effect should be yielded in.

Usually, the camera transform is called what places the camera object into the world, i.e. the transformation from the camera local space into the global space. Also usually the view transform is the inverse of the camera transform, i.e. the transformation from the global space into the camera local (a.k.a. view) space.

With the above definition and the usage of column vectors, a camera transform is often build up as

C := T * R * S

what you will call

translation mul rotation mul scaling

but actually means

scaling on the mesh, rotating the scaled mesh, translating the rotated scaled mesh

The corresponding view transform is then

V := C-1 = S-1 * R-1 * T-1

where, if you stores the matrices as view matrices, you say

scaling mul rotation mul translation

Now, the same game with row vectors gives you

C := S * R * T

so that the order is reversed. This is true for all derived matrices, but the meaning is left as is! E.g. the above C actually still means

scaling on the mesh, rotating the scaled mesh, translating the rotated scaled mesh

This is the difference of column vs row vector math.

In the end you see that both orders are valid in both systems, depending of what you speak of. Furthermore, you can think of applications that are not as easy as the composite of 3 matrices above, giving perhaps other orders in both systems. Whenever you read about transformation matrices you must realize the convention used in the reading, or else you cannot exactly interpret what you read.

Hope that helps. Matrix math is a bit confusing if the caveats are not known.

Edited by haegarr, 17 December 2013 - 03:27 PM.

### #3Believe82  Members

Posted 17 December 2013 - 03:30 PM

Oh I got it! I was thinking of the view transform and the camera transform as one in the same. Thanks a lot!

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