While the transform is conceptually straightforward, algorithms of doing the conversion vary significantly in speed, numerical precision and parallelism.
[1] These matter because macromolecular chains, such as polymers, proteins, and DNA, can have thousands of connected atoms and atoms consecutively distant along the chain that may be close in Cartesian space (and thus small round-off errors can accumulate to large force-field errors.)
The optimally fastest and most numerically accurate algorithm for conversion from torsion-space to cartesian-space is the Natural Extension Reference Frame method.
The Z-matrix representation is often preferred, because this allows symmetry to be enforced upon the molecule (or parts thereof) by setting certain angles as constant.
The Z-matrix simply is a representation for placing atomic positions in a relative way with the obvious convenience that the vectors it uses easily correspond to bonds.