### Understanding Best Fit Alignments

To properly create your Best Fit alignment, consider the information presented here:

A Best Fit alignment is, first of all, an alignment that causes a set of measured points or a set of actual feature centroids to match, as closely as possible to its nominal location or theoretical counterpart. In certain cases it is also possible for a Best Fit alignment to optimally match a set of points to a CAD curve or surface.

The Least Squares algorithm of the Best Fit alignment aligns the two point sets by transforming one of the sets so that the sum of the squared distances between matching points in the two sets is minimal. To understand how the Least Squares alignment works, visualize a spring (of initial length zero) between each measured point and its nominal counterpart. The springs are stretched as the distance between the two points increases. The position the point set ends up in when you release it and let the springs act is the solution to the Least Squares alignment problem.

Similarly, the Min/Max algorithm aligns two point sets by minimizing the maximum distance between matching points in the two sets. After a Min/Max alignment, the maximum distance is exhibited by enough point pairs (usually three), in enough directions so that any change in the position of either set would cause an increase in distance between at least one pair of points. In PC-DMIS, Min/Max alignments are strictly 2D.

However, sometimes there might be preferred directions in which to align the two point sets. For instance, if the points are on the surface of a car hood or on its boundary, then motion along the surface or along the boundary is not as important as motion in a perpendicular direction. The Vector fit algorithm gives you some control over preferred directions by minimizing the squared lengths of the distance vectors projected onto the given nominal vectors.

In all three cases (Min/Max, Least Squares, and Vector fit), weights can be specified by the user and/or generated from tolerances. A point with a larger weight is given more priority in optimizing the alignment.

Best Fit alignments will exclude from their calculations any features that were skipped during part program execution. When this occurs, PC-DMIS displays a message informing you that one or more (or all) features used by an alignment were skipped during execution.

The following topics will help you to understand important aspects of Best Fit alignments.

More:

Comparing Best Fit Alignments

2D Best Fit Command Line Format

3D Best Fit Command Line Format

2D or 3D Best Fit Alignments

Available Best Fit Types

Constraints for 3D Best Fit Alignments

Feature Weights

Constructed Feature Sets and Curves as Best Fit Alignment Inputs

Scans as Best Fit Alignment Inputs

Tagged Features in a Feature Set or Scan

3D Alignment Center of Rotation

Point Set to CAD Alignments