Worked to improve the orientation and disorientation calculator. While in the case of parameterization Rodriguez Vector representation does not cause many problems , apart from the need to become familiar with the shape of the primary zones for orientation and disorientation , the Euler parameterization of a challenge. The first observation is that the data supplied from the TSL program in the form of a matrix orientation expressed as Euler angles ( φ1 , Φ , φ2 ) are not brought to the area of ​​basic orientation . Perhaps it can be set in the program, but due to the difficult access to equipment and generalization of the calculation in the calculator and so it is impossible to avoid these transformations . The fact that the orientations are not reduced to the primary area can be seen at the level of individual grains which have a consistent orientation of the domain . Such grains can not be described on average one three numbers ( φ1 , Φ , φ2 ), but his relationship orientation has n equivalence classes (n depend on the symmetry of the crystallites ) , due to the lack of conversion to one particular area of ​​the primary .
The next problem was how to draw Euler angles of the rotation matrix . Angles drawn in accordance with the formula φ1 = ArcTan [- g [ [ 3, 2 ]] g [ [ 3, 1 ]]] , Φ = ArcCos [g [ [ 3, 3 ]]] , φ2 = ArcTan [g [ [ 2, 3 ] ] , g [ [ 1, 3 ]]] , where the function ArcTan meant extensive arkus tangent , taking into account the sign of expressions. Then had properly wrap Euler angles , as these drawn from the matrix of rotation could be negative. The first step was to add or subtract one period 2π , that is modulo 2π to perform an operation on each of the angles. Then , if the angle Φ exceeded π , to be added to φ1 and φ2 value of π , and for the new Φ recognize the value of 2π - Φ . Then again , of course, had to bring the angles φ1 and φ2 to φ1 numbers mod ( 2π ) and φ2 mod ( 2π ) .