I perform microstructural simulations and consider a polycrystal with cubic lattice. Each grain characterizes by its coordinate system Cc, which is somehow oriented relative to the global (specimen) coordinate system Cs. The orientation is expressed in terms of direction cosines. I need to construct an orientation matrix g consisting of three orthogonal vectors: Cc = g * Cs. The question is how I should order my three unit vectors in the orientation matrix. Should I put the unit vector with the maximum x coordinate in the first row, the unit vector with the maximum y coordinate in the second row and so on?
Your matrix should present an right hand system. Therefore, after choosing 2 unit vectors the 3rd one should be the cross product. If you change the sequence of the first 2 unit vectors this will change the sign of the 3rd one.
Dear Prof. Manfred Staat,
Thank you for your answer. It was really helpful.
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