PolygonMoment

void fil::PolygonMoment
(
	const fil::Path& inPolygon,
	fil::PolygonMomentType::Type inMomentType,
	bool inCentral,
	float& outMoment,
	float& outNormMoment
)

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.

List of possible exceptions:

Error type	Description
DomainError	Not supported moment type in PolygonMoment.
DomainError	Open path on input in PolygonMoment.

• 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.