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# Another Matrix Order Question :)

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### #1wsderf  Members

Posted 13 April 2012 - 10:04 AM

I'm trying to get my head around row/column major matrices and row/column vectors. Mostly, I'm using the following for reference:
http://www.j3d.org/matrix_faq/matrfaq_latest.html

So, trying to write a 4x4 matrix class, I have a class with an array of values:

float m_Values[16];

Now, I'm going to be using column vectors, so:

1) Am I right in saying the following:

Multiplication should be written like so: Matrix * Vector
Combining rotation matrices should be written (for example): Projection * View * World

2) Row/Column major matrices refers to the order the data is stored in memory, NOT whether or not the translation component should be down the right hand side / along the bottom.

The translation is down the right hand side of the matrix when using column vectors, and across the bottom when using row vectors. Is this correct?

3) OpenGL uses column vectors, and uses column major matrices, and we want to upload the matrices to OpenGL using glUniformMatrix4fv

I'm pretty sure this is right, so does that mean that the translation component should be in m_Values[12], m_Values[13] and m_Values[14]?

4) When multiplying two matrices together, the operator* should have something like the following

final.m_Values[0] = (this.m_Values[0] * other.m_Values[0]) + (this.m_Values[1] * other.m_Values[4]) + (this.m_Values[2] * other.m_Values[8]) + (this.m_Values[3] * other.m_Values[12]);

final.m_Values[1] = (this.m_Values[0] * other.m_Values[1]) + (this.m_Values[1] * other.m_Values[5]) + (this.m_Values[2] * other.m_Values[9]) + (this.m_Values[3] * other.m_Values[13]);

final.m_Values[2] = (this.m_Values[0] * other.m_Values[2]) + (this.m_Values[1] * other.m_Values[6]) + (this.m_Values[2] * other.m_Values[10]) + (this.m_Values[3] * other.m_Values[14]);

I'm not sure if this order is right, or if I need to multiply a different way because the matrices are stored in column major order in memory. Can anyone clarify if this is the right way or not?

5) The Matrix Quaternion FAQ I linked to at the top seems to be using column vectors, so vectors are multiplied on the right, as shown in Q13 of the FAQ. Q35 appears to suggest that matrices should be multiplied the other way though.

Q35 states that in order to get an X rotation, followed by a Y rotation, followed by a Z rotation, you multiply:

M = X.Y.Z

But I thought that, because it is using column vectors, the first transformation should be at the right hand side. I.e.:

M = Z.Y.X

In fact, looking at the function calls listed at the start of Q36, it seems to be multiplying in the order I'd think was correct (i.e. Z * Y * X), but still goes on to state that M = X.Y.Z.

Are Qs 35 & 36 wrong, or is it just a difference in notation for multiplying matrices instead of vectors (as Q13 says that V' = M.V, which seems like the right way round to me). Or is it just that I'm very confused? ;)

Hopefully someone can help me out on this, it would be very useful. Thanks

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