In a GD&T class, I often talk about (and sketch) how a sample part can be held in a fixture — this helps people understand the concept of datums, particularly if datum targets are involved.
This does not imply that an inspector must use a customized fixture to check a part. I refer to fixtures and physical gaging in a class simply because people can visualize those concepts, whereas a CMM is more abstract (sometimes CMMs and similar devices are called “soft gaging” as opposed to traditional “hard gaging”).
If you are using a CMM, then you ensure that the probe samples the part at the prescribed datums; this establishes a coordinate system in the computer for other measurements to be made against. But wait: the part isn’t floating around in mid-air! It is still contacting something. Perhaps it is sitting on a granite table. Here’s a key point: instead of sampling three points on the surface of the part to create the datum, you should take three points on the table, since that table simulates the true datum (as derived from the high points of the part surface).
The only tricky part is when datum targets are involved. This is where the designer identifies specific points, lines, or areas on a surface which are to be sampled for constructing a datum in the computer. It’s tricky because those targets have an exact location, which should be dimensioned from other datums (or somehow located in the math model). But you can’t probe all datums simultaneously, so this is where a fixture might help!
Without a fixture, you might sample three pads representing A1, A2, and A3. But if your location for those three pads was off, you won’t know it until you sample B and C. So it’s doable, but it becomes an iterative process; you may have to resample some datum targets until you determine that the sampled points were at the prescribed locations.
Note to engineers/designers: This is one reason why it’s not ideal to place datum targets at random locations! They are not identifiable to the eye. Also, the datum targets should simulate the actual function or contact points, and random locations don’t do that. (But they are sometimes necessary if the functional points are inaccessible or if the geometry of the part is so complex that there’s no other way around it.)