Algorithms for deriving crystallographic space-group information. II. Treatment of special positions

Algorithms for the treatment of special positions in three-dimensional crystallographic space groups are presented. These include an algorithm for the determination of the site-symmetry group given the coordinates of a point, an algorithm for the determination of the exact location of the nearest special position, an algorithm for the assignment of a Wyckoff letter given the site-symmetry group, and an alternative algorithm for the assignment of a Wyckoff letter given the coordinates of a point directly. All algorithms are implemented in ISO C++ and are integrated into the Computational Crystallography Toolbox. The source code is freely available.