A correct transformation matrix (which is a 2D entity) according to math literature:
R11 R12 R13 Tx R21 R22 R23 Ty R31 R32 R33 Tz 0 0 0 1 That matrix stored in column-major order in 1D memory: R11 R21 R31 0 R12 R22 R32 0 R13 R23 R33 0 Tx Ty Tz 1 That matrix stored in row-major order in 1D memory: R11 R12 R13 Tx R21 R22 R23 Ty R31 R32 R33 Tz 0 0 0 1 If these are the things you dispute, that is an easier argument to deal with. Otherwise my response follows: 2009/1/15 Paul Fotheringham <[email protected]> [...] > > Eh? By what definition exactly? http://fly.cc.fer.hr/~unreal/theredbook/appendixg.html http://www.opengl.org/documentation/specs/man_pages/hardcopy/GL/html/gl/translate.html http://www.opengl.org/documentation/specs/man_pages/hardcopy/GL/html/gl/rotate.html Rotation matrix order: http://en.wikipedia.org/wiki/Rotation_matrix Which is the order in the OpenGL man pages. If you create a simple rotation matrix in OSG and compare it to there, you'll see that it's transposed according to this definition. > OpenGL is neither row-major or column-major. http://en.wikipedia.org/wiki/Row-major_order You can't store a well-defined multidimensional entity in one dimensional storage and say it's neither. If you do, the definition of the multidimensional entity becomes open to interpretation. Which actually is not, as explained in the next paragraph. > It treats a transformation matrix as 16 floats, nothing more. Only when one > imposes a 4x4 structure of rows and columns on the 16 numbers does one then > encounter the question "Which way shall I order them?". At that point you > choose row-major or column-major as the description of how your data is > stored in the matrix. Yes, and the definition of the matrix multiplication operator in OSG makes it clear that the first index of the array is rows and second index is columns. Also if you look at the code closely, the first index is always referred to as rows. So, when you treat the indices as such, you see that the matrix being stored is actually a transposed version of a transformation matrix. Hence, you have to treat them as transposed transformation matrices to get your math right. > > > There is no such > > thing as > > "row-major matrix" since matrices are > > mathematical entities that have > > nothing to do with storage. > > Yes there is, I've just described it above. It's storage that has nothing > to do with it i.e. OpenGL's view of it as 16 numbers, it's how you construct > your mathematical entity, your matrix, that imposes one view or the other. You don't construct the mathematical entity of transformation matrices based on how OpenGL stores matrices. The mathematical definition in the literature is clear, which is also used in the OpenGL man pages when talking about transformation matrices. I know it sucks, but it's just the way it is. -Gazi
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