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Correct matrix layout documentation 

Actually, both OpenGL and DirectX specify a matrix layout where the base vectors and the translational
part is consecutive in memory.
OpenGL uses post-multiplication of column-vectors and stores the matrix in column-major storage format:

    | X1  Y1  Z1  T1 |  | a |
    | X2  Y2  Z2  T2 |  | b |
    | X3  Y3  Z3  T3 |  | c |
    |  0   0   0   1 |  | 1 |

DirectX on the other hand uses row-major storage format but also pre-multiplication of
row-vectors

    | a b c 1 | | X1  X2  X3  0 |
                | Y1  Y2  Y3  0 |
                | Z1  Z2  Z3  0 |
                | T1  T2  T3  1 |

So a matrix is stored the same way in both frameworks and both times the translational part is consecutive,
which is not the format that Assimp uses.
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Manuel Freiberger 2018-01-11 20:58:47 +01:00 committed by GitHub
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@ -566,19 +566,22 @@ A typical 4x4 matrix including a translational part looks like this:
X1 Y1 Z1 T1
X2 Y2 Z2 T2
X3 Y3 Z3 T3
0 0 0 1
0 0 0 1
@endcode
with <tt>(X1, X2, X3)</tt> being the image of the X base vector, <tt>(Y1, Y2, Y3)</tt> being the image of the
Y base vector, <tt>(Z1, Z2, Z3)</tt> being the image of the Z base vector and <tt>(T1, T2, T3)</tt> being the
translation part.
All matrices in the library are row-major. That means that the matrix elements are stored row by row in memory,
which is identical to the OpenGL matrix layout. So the above matrix is stored in memory as
<tt>[X1, Y1, Z1, T1, X2, Y2, Z2, T2, X3, Y3, Z3, T3, 0, 0, 0, 1]</tt>. If you want to use these matrices
in a framework, which expects the matrix layout to be column-major (stored along the columns), such as
DirectX or Matlab, you will have to transpose the matrix first.
with <tt>(X1, X2, X3)</tt> being the local X base vector, <tt>(Y1, Y2, Y3)</tt> being the local
Y base vector, <tt>(Z1, Z2, Z3)</tt> being the local Z base vector and <tt>(T1, T2, T3)</tt> being the
offset of the local origin (the translational part).
All matrices in the library use row-major storage order. That means that the matrix elements are
stored row-by-row, i.e. they end up like this in memory:
<tt>[X1, Y1, Z1, T1, X2, Y2, Z2, T2, X3, Y3, Z3, T3, 0, 0, 0, 1]</tt>.
To be very precise: The transposition has nothing to do with a left-handed or right-handed coordinate system
but 'converts' between row-major and column-major storage format.
Note that this is neither the OpenGL format nor the DirectX format, because both of them specify the
matrix layout such that the translational part occupies three consecutive addresses in memory (so those
matrices end with <tt>[..., T1, T2, T3, 1]</tt>), whereas the translation in an Assimp matrix is found at
the offsets 3, 7 and 11 (spread across the matrix). You can transpose an Assimp matrix to end up with
the format that OpenGL and DirectX mandate. To be very precise: The transposition has nothing
to do with a left-handed or right-handed coordinate system but 'converts' between row-major and
column-major storage format.
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