# Is it possible to remove specifications naturally

## Align and Shape Removal

### Assignment

Assignment is an operation in which a mathematical model is configured that best fits a real workpiece, which is usually represented as a point cloud. Models are geometric shapes (straight line, plane, part of a sphere, cylinder, cone, polynomial, etc.).

The assignment methods used in the field of surface metrology are:

- Least squares of error, simple or total, limited or not;
- Minimum zone;

The least squares method complies with the L2 standard because it minimizes squared deviations. The minimal zone method corresponds to the L∞ norm, which is also called the Chebyshev norm. The L1 norm is sometimes used by minimizing absolute height values or simply by averaging the heights.

Constraints used at the same time allow the radius of a sphere to be determined and the position of the center to be calculated, or the level of the least squares to be shifted outside of the material, i.e. brought into contact with the highest point of the surface.

Least squares symbols are LSLI (for a straight line) or LSPL (for a plane).

In the **Minimal zone method** the profile is enclosed between two parallel straight lines, or the surface between two parallel planes; an attempt is made to find the best orientation that minimizes the distance between the two straight lines (or both planes). Symbols for the minimal zone method are MZLI and MZPL.

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