What is the most efficient method for determining if two features (points, lines, or polygons) are geometrically identical? I'm not concerned about a square figure that contains eight vertices (four corners and vertices at segment midpoints) being flagged as identical to a "true" square (four corners and no vertices at segment midpoints).
Potential gotchas are the order of the vertices and direction of line or polygon. Suppose one square is defined starting in the northwest corner and another square starts in the southeast. Coordinates of the vertices and all other properties are identical. I would expect these to be a match since just the order of vertices is just different. Or what if one square is defined clockwise but the other counter-clockwise? Again, this shouldn't matter.
What is the most efficient way to find if the two are identical?