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schupf

OpenGL OpenGL Matrix

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schupf    221
Hello,

I am reading a book called "OpenGL SuperBible 5th Edition" and the page 158 tries to explain matrices.
Actually I have a solid understanding of matrices (worked a lot with Direct3D), but this page confuses me.
The code is about a spinning torus:
m3dTranslationMatrix44(mTranslate, 0, 0, -2);
m3dRotationMatrix44(mRotate, yRot, 0, 1, 0);
m3dMatrixMultiply44(mModelview, mTranslate, mRotate);
m3dMatrixMultiply44(mModelViewProjection, mProjectionMatrix, mModelView);

I looked at the code and tried to figure out the order of the multiplication. Since the torus is spinning around itself I thought the multiply function multiplies the 3rd argument with the 2nd argument. Thus the 3rd transformation is applied prior to the 2nd transformation. This would also explain the last code line, because the modelView Transformation has to be applied BEFORE the projection.

But now I have to read this in the book:
Quote:
Remember, the order of operations is important, and here we first translate and then rotate the torus.
m3dMatrixMultiply44(mModelview, mTranslate, mRotate);
It should now be out in front of us and spinning in place...

What? If we FIRST translate and then rotate the torus will not rotate around itself rather around the origin.

Is this an error in the book or do I confuse something?

[Edited by - schupf on October 16, 2010 5:18:47 PM]

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Laval B    12387
Hello

With the OpenGL API, the matrices are column major. They are passed as an array of 16 floats (float matrix[16]) which means the elements of a matrix are ordered as follow

a0 a4 a8 a12
a1 a5 a9 a13
a2 a6 a10 a14
a3 a7 a11 a15

where the index is the index in the float array. That implies that the order of multiplication is the oposite of that used by the Direct3D API where matrices are row major.

Hope this helps.

Laval Bolduc

[Edited by - Laval B on October 16, 2010 8:16:24 PM]

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jyk    2094
Quote:
Original post by Laval B
With the OpenGL API, the matrices are column major. They are passed as an array of 16 floats (float matrix[16]) which means the elements of a matrix are ordered as follow

a0 a4 a8 a12
a1 a5 a9 a13
a2 a6 a10 a14
a3 a7 a11 a15

where the index is the index in the float array. That implies that the order of multiplication is the oposite of that used by the Direct3D API where matrices are row major.
Actually, that's not correct; matrix storage order doesn't (necessarily) imply anything about multiplication order.

What you're thinking of is vector notation convention (mathematically, row vectors are multiplied to the left of matrices and column vectors to the right).

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TheBuzzSaw    143
Keep in mind that the matrices work BACKWARD from the way we would logically think of them. Reading your statement as plane English, you are correct: it makes no sense that translating THEN rotating would make the torus rotate about itself in front of the camera. However, you have to start with the torus and work backward through the matrices. With that perspective, it makes sense. It rotates first. Then it moves away. That would make it "rotate about itself".

LOGIC -- rotate, translate, move world (camera), projection
CODE -- projection, move world, translate, rotate

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schupf    221
Quote:
Original post by TheBuzzSaw
Keep in mind that the matrices work BACKWARD from the way we would logically think of them. Reading your statement as plane English, you are correct: it makes no sense that translating THEN rotating would make the torus rotate about itself in front of the camera. However, you have to start with the torus and work backward through the matrices. With that perspective, it makes sense. It rotates first. Then it moves away. That would make it "rotate about itself".

LOGIC -- rotate, translate, move world (camera), projection
CODE -- projection, move world, translate, rotate

Thanks! That helped me a lot. I was used to the Direct3D matrices and to be honest I also find the D3D matrix order much more intuitive, cause the logical (plain english) order is the same as the mathematical order.

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haegarr    7372
Quote:
Original post by schupf
... cause the logical (plain english) order is the same as the mathematical order.
People using a right-to-left script system may claim that "logical order" doesn't match "english order". Moreover, from the mathematical point of view, neither the one nor the other writing is incorrect or even more senseful than the other.

If you look at a 2 step transformation of a vertex v for row vectors
vr' := vr * Rr * Tr
and you look at the same transformation for column vectors
vc' := Tc * Rc * vc
then you'll notice that in both formulas the R is closer to the v than T is. This is the only important aspect! Because a transformation closer to the vector is applied in a space "more locally" than the other transformations. Hence, the transformation closest to the vector seems to be applied first, what may be expressed like so
vr' = ( vr * Rr ) * Tr
resp.
vc' = Tc * ( Rc * vc )
(although mathematically it plays no role how to set the parentheses).

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schupf    221
I know haegarr, but for ME row vectors (and the according "row matrices") feel more intutive.
When I want to apply a scale, then rotate than translation, I would intuitively write this on a paper:
v*S*R*T, because I read from left to write.
And thats exactly the order I set the matrices in D3D. In OpenGL I had to switch the order around, thus I have to set the T matrix first, even though mathematically it is applied last.
I know that most mathematician will probably prefer the OpenGL matrix order, but I don't like it.

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jyk    2094
Quote:
Original post by schupf
I know that most mathematician will probably prefer the OpenGL matrix order, but I don't like it.
Fortunately, in many if not most cases, you can use whichever convention you prefer :) With OpenGL for example, you can use either row vectors or column vectors (as long as you use a math library that supports your preferred convention).

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