ShapeMoment

void avl::ShapeMoment
(
	const avl::Path& inShape,
	avl::ShapeMomentType::Type inMomentType,
	bool inCentral,
	atl::real& outMoment,
	atl::real& outNormMoment
)

void ShapeMoment
(
	AvlNet.Path inShape,
	AvlNet.ShapeMomentType inMomentType,
	bool inCentral,
	out float outMoment,
	out float outNormMoment
)

The operation computes the mathematical features of a shape 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 shape surface, while \( p_x \) and \( p_y \) denote, accordingly, x and y coordinate of a point.

When inCentral parameter is set, the shape is shifted before computations so that its mass center is at location (0,0).

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

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

ImageMoment, RegionMoment