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OpenGL Matrix layout in OpenGL, DirectX and AGAL

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Hello. I'm totally stuck in vector and matrix multiplication. I can't sleep 2 days - there're matrices in my head. AGAL - Adobe Graphics Assembly Language - is used in stage3D API in ActionScrips. And it's beast. I don't know OpenGL and DirectX, and it hard to say what AGAL is similar to. I know, for example that it uses right handed coordinate system - i.e. like in DirectX. But I can't say anything about matrices. Here's documentation about vector and matrix multiplication:

[quote]destination.x = (source1.x * source2[0].x) + (source1.y * source2[0].y) + (source1.z * source2[0].z)
destination.y = (source1.x * source2[1].x) + (source1.y * source2[1].y) + (source1.z * source2[1].z)
destination.z = (source1.x * source2[2].x) + (source1.y * source2[2].y) + (source1.z * source2[2].z)[/quote]


Here source1 is vector and source2 is matrix (actualy array of vectors). Documentation doesn't say what side from matrix the vector is - from left or right. I write down on paper this multiplication and this is what I get:

Here multiplication like in DirectX - row vector which means that matrix have row layout
[font=courier new,courier,monospace]........|x0 y0 z0|
|x y z| |x1 y1 z1| = |x * x0 + y * x1 + z * x2, x * y0 + y * y1 + z * y2, x * z0 + y * z1 + z * z2|
........|x2 y2 z2|[/font]
And it differs from documentation.

Ok, let's try OpenGL rule - column layout matrix and column vector
[font=courier new,courier,monospace]|x0 x1 x2| |x|
|y0 y1 y2| |y|[/font][font=courier new,courier,monospace] = |x * x0 + y * x1 + z * x2, x * y0 + y * y1 + z * y2, x * z0 + y * z1 + z * z2|[/font]
[font=courier new,courier,monospace]|z0 z1 z2| |z|[/font]
Same as before - not as in documentation.

But if I transpose matrix - all fine - documentation and paper calculations are the same. And my question is - is it legal to multiply row vector wit column-layout matrix and column vector with row-layout matrix? I've digged tons of literature but I can't remember I saw this anywhere.

P.S.: I tried to write as clear as I can, but if there're any questions please ask. I need to solve this problem. Edited by Volgogradetzzz

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Stage3D should sort this out for you, you just need to upload a valid matrix or vector.<Number> and it will ensure it works fine on DirectX and OpenGL.

If you use the matrix3d class that is inbuilt just make sure you always set the transpose flag when you upload it.

Consistency is the key here, if using transposed matrices, then always do, don't mix and match :)

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Whether the matrix is row or column major has nothing to do whether you can multiply it with a vector or not. The major-ness of a matrix is only a way to determine how a matrix is converted from a 2-dimensional entity to a 1-dimensional layout for storage in memory. It tells you where in the memory you find the different values of the matrix. The matrix itself is still the same matrix no matter what major-ness you use or where, or how, you store the actual values. What has to change in your code when you change major-ness is only how you access the elements of the matrix.

edit: And as bwhiting said before me: consistency is the key. Know what you're doing, and do it consistently. If you define a specific major-ness, then you need to ensure that you access your matrix according to that rule. Similarly, if you define for example column vectors, then you can only multiply them from the right, but major-ness is, from a mathematical point of view, totally irrelevant to the actual multiplication. Edited by Brother Bob

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Wow, so fast.
Ben, I don't want use matrix3D for several reasons so I'm trying to pass matrix through 4 calls of setVertexVectorConstant().
Bob, I read your previous great posts but I mean no major-ness of matrix but layout. For example rotation matrix in DirectX have it's rows as basis, In openGL basis are columns. Or take a translational part of 4x4 matrix. If we have vector on the left the translational vector in matrix should be exactly 4-th row - it cannot be 4-th column or we get wrong results. In my example I pass 4 vectors and they should form a matrix. But if you write this vector either as rows or columns and multiply by some vector you wil not get the answer like in documentation. And I'm very interesting why?

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I misuderstood your question then. But re-reading it again with the new context, I'm not sure what it is you're asking. Is it that it seems like the OpenGL and Direct3D matrices has to be transposed to match the operations performed by AGAL?

In that case, it could simply be that AGAL uses different vectors and matrix major-ness. That would mean that, for example, source2[0] in the code from your first post is in fact not the first basis vector, but a vector of the x-components of all basis vectors. That is a result of using a mixed vector and matrix major-ness.

This is not the same as having column vectors and a matrix with row-basis vector or vice versa. It's just that the matrix is ordered differently in memory compared to OpenGL or Direct3D. It is in no way wrong and as I said in my first post it is entirely about defining where the elements go in the memory. OpenGL and Direct3D both have the basis vectors of their matrices linearly in memory, but if my assumption here is correct then AGAL does not have its basis vectors linearly in memory as a result of different basis-ness and major-ness. Edited by Brother Bob

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Thanks, Brother Bob, it makes sence. But there're still many questions. source2[0] is basis vector for sure. And it seems that there're mistake in documentation (quote in 1st post). Anyway I made some tests and it looks like we have column-layout matrix and so column vectors. So we have DirectX-like coordinate system and OpenGL-like matrix operations. Best from both worlds.

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