Most of the time form measurement looks at basic geometrical shapes: how round something is, how straight or even how flat it is. You measure a cylinder and make a trace up the side to see if it’s straight; you take a polar trace to see if it’s round; you combine a number of these traces to see if it’s cylindrical. All these are basic geometries: lines, planes, circles and cylinders.
But all of us have known since we got our first Fisher-Price play set that the square peg doesn’t fit in the round hole. And sometimes, round pegs don’t even fit in round holes. That is the reason for roundness specifications on many parts: to know if a round “peg” is round enough to fit into a round “hole” on parts being assembled. However, sometimes just knowing if it’s round isn’t good enough, either. In the real three-dimensional world where precision machined parts have to function, it might be important to understand how the shape of the errors in roundness will impact the desired function of the surface.