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Module: | FoundationBasic |
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Computes the area of a polygon divided by the area of a circle having the same feature.

Name | Type | Description | |
---|---|---|---|

inPolygon | Path | ||

inCircularityMeasure | CircularityMeasure | ||

outCircularity | Real |

### Description

Circularity is a measure of similarity of a polygon to the perfect circle. Circular polygons have circularity close to 1.0, while the more elongated the shape is (or contains more holes), the closer to 0.0 is its circularity.

Mathematically, the circularity is calculated as follows:
Where **c** denotes a
circular polygon having the same feature as input polygon **s**. The feature being considered depends on the inCircularityMeasure chosen and it is:

- the minimal bounding circle in case of
**BoundingCirclePreserving** - the perimeter in case of
**PerimeterPreserving** - the radius (maximal distance from mass center to any of the shape points) in case of
**RadiusPreserving**

Note that if the input path is not a valid polygon (i.e. it has at least one self-intersection), the computation may lead to results that are not intuitive.

### Examples

### Errors

This filter can throw an exception to report error. Read how to deal with errors in Error Handling.

List of possible exceptions:

Error type | Description |
---|---|

DomainError |
Degenerate polygon on input in PolygonCircularity. |

DomainError |
Not supported circularity measure in PolygonCircularity. |

DomainError |
Open path on input in PolygonCircularity. |

### Complexity Level

This filter is available on **Advanced** Complexity Level.

### See Also

- RegionCircularity – Computes the area of a region divided by the area of a circular region having the same feature.

- PolygonConvexity – Computes the area of a polygon divided by the area of its convex hull.

- PolygonElongation – Computes the elongation factor of a polygon (perfect circle has minimal elongation equal 1.0).