Start » Filter Reference » Path » Polygon Features » PolygonMoment
Advanced| Module: | FoundationBasic |
|---|
Computes the selected second-order moment of a polygon in regular and normalized ( divided by polygon area ) variant.
| Name | Type | Description | |
|---|---|---|---|
 |
inPolygon | Path | |
|
inMomentType | PolygonMomentType | |
|
inCentral | Bool | |
 |
outMoment | Real | |
|
outNormMoment | Real |
Description
The operation computes the mathematical features of a polygon called moments. Those are integrals computed as follows:
\[ \begin{aligned} Moment_{2,0}(S) &= \int_{S} p_x^2 \\ Moment_{1,1}(S) &= \int_{S} p_x p_y \\ Moment_{0,2}(S) &= \int_{S} p_y^2 \end{aligned} \]The integration is conducted over polygon surface, while \( p_x \) and \( p_y \) denote, accordingly, x and y coordinate of a point.
When inCentral parameter is set, the polygon is shifted before computations so that its mass center is at location (0,0).
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.
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 | Not supported moment type in PolygonMoment. |
| DomainError | Open path on input in PolygonMoment. |
Complexity Level
This filter is available on Advanced Complexity Level.
See Also
- RegionMoment – Computes selected second-order moment of a region in regular and normalized ( divided by region area ) variant.
- ImageMoment – Computes the selected moment of an image in regular and normalized (divided by sum of pixel values) variant.