#### Comparing Best Fit Alignments

Least Squares Fit

The Least Squares fit minimizes the sum of the squared errors, which is the same as minimizing the average squared error. A weighted Least Squares fit minimizes a weighted average of the squared errors. It can be 2D or 3D in PC-DMIS.

Vector Fit

The Vector fit is a kind of Least Squares fit, except that the error vectors are projected onto given direction vectors (usually the normals), and these projected distances are used in the Least Squares fit. If the normal vectors are used, then motion perpendicular to the normal is allowed without affecting the "goodness" of the fit. This can be used to mimic a hard gage.

Min Max Fit

Currently, PC-DMIS only allows 2D Min/Max fits. A Min/Max fit minimizes the maximum error. For this reason it can be used in an accept/reject procedure—if the maximal error is small then all errors are small, whereas a small least squares error, being an average, doesn't guarantee that all errors are small.

If weights based on tolerances are used then a Min/Max fit reduces the percentage of available tolerance used by each feature. The Least Squares fit reduces the "average" amount of tolerance used by all features. Since the weights generated are reciprocals of the tolerances, a feature with a relatively small weight (or lower priority) corresponds to a large tolerance zone, which gives it more freedom to move without affecting the other features. A feature with a relatively large weight (or small tolerance zone) gets a high priority in the alignment process.