This section describes the class Miller and gives an overview how to deal with crystal directions in MTEX. Crystal directions are represented in MTEX by the variables of the class Miller which in turn represent a direction with respect to the crystal coordinate system. described by three or four values h, l, k (,m) and a crystall symmetry. Essentially all operations defined for the vector3d class are also available for Miller indece. Furthermore, You can ask for all crystallographically equivalent crystal directions to one Miller indece. Miller indice are definded by three coordinates h, k, l (four in the case of trigonal or hecagonal crystal symmetry) and by the corresponding symmetry class. It is also possible to convert a vector3d object into a Miller indice. Miller indece are plotted as spherical projections. The specific projection as well as wheter to plot all equivalent directions can be specified by options. By providing the options all and labeled all symmetrically equivalent crystal directions are plotted together with there correct Miller indice. A simple way to compute all symmetrically equivalent directions to a given crystal direction is provided by the command symmetrise The command eq or == can be used to check whether two crystal directions are symmetrically equivalent. Compare The angle between two crystal directions m1 and m2 is defined as the smallest angle between m1 and all symmetrically equivalent directions to m2. This angle in radiand is calculated by the funtion angle Converting Miller indice into a three dimensional vector is straight forward using the command vectord3d. one can apply it to a crystal direction to find its coordinates with respect to the specimen coordinate system By applying a crystal symmetry class one obtains the coordinates with respect to the specimen coordinate system of all crystallographically equivalent specimen directions. Source.