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Does Least-squares (LSQ) simulate perfect roundness?

Is it fair to consider the LSQ evaluation of a diameter to be it's value at "perfect" roundness? We go back and forth about what to do with non-rigid parts with regards to roundness. Some want to use a fixture to constrain the part while others want to use LSQ to virtually constrain the part. Using a scanning CMM and taking enough points with proper filtering, can a least square best-fit evaluation be considered as virtually constraining a part to perfect form?
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