(analytic geometry, topology, countable) The designation of a parametrised curve as "positively" or "negatively" oriented (or "nonorientable"); the analogous description of a surface or hypersurface.
“The temple's orientation was such that the sun's rays would penetrate it directly only twice a year.”
“Do we really still get our orientation by turning towards the east? And still regard the points of the compass as our defining coordinates?”
“Before we can consider this point about the orientation of the statue, it is necessary to determine the exact position of the temple before which it is supposed to have stood.”