On the general transformation from molecular geometric parameters to cartesian coordinates

This article presents a general method and accurate algorithm for calculating the Cartesian coordinates (x_a, y_a, z_a) from an arbitrary triple of distances r(a,i), angles, θ(a,j,k), or dihedral angles ?(a,l,m,n), specifying the position of the nucleus a relative to nuclei i, ?, n with known Cartesian coordinates. There is a brief discussion of the requirements on the 3N-6 geometric parameters in order for them to determine the shape of an N-atomic molecule.