  A protein is traditionally visualised as a piecewise linear discrete curve,
and its geometry is conventionally characterised by the extrinsically
determined Ramachandran angles. However, a protein backbone has also two
independent intrinsic geometric structures, due to the peptide planes and the
side chains. Here we adapt and develop modern 3D virtual reality techniques to
scrutinize the atomic geometry along a protein backbone, in the vicinity of a
peptide plane. For this we compare backbone geometry-based (extrinsic) and
structure-based (intrinsic) coordinate systems, and as an example we inspect
the trans and cis peptide planes. We reveal systematics in the way how a cis
peptide plane deforms the neighbouring atomic geometry, and we develop a
virtual reality based visual methodology that can identify the presence of a
cis peptide plane from the arrangement of atoms in its vicinity. Our approach
can easily detect exceptionally placed atoms in crystallographic structures.
Thus it can be employed as a powerful visual refinement tool which is
applicable also in the case when resolution of the protein structure is limited
and whenever refinement is needed. As concrete examples we identify a number of
crystallographic protein structures in Protein Data Bank (PDB) that display
exceptional atomic positions around their cis peptide planes.
