moments_points_xldmoments_points_xldMomentsPointsXldMomentsPointsXldmoments_points_xld (Operator)

Name

moments_points_xldmoments_points_xldMomentsPointsXldMomentsPointsXldmoments_points_xld — Geometric moments , , and of contours or polygons treated as point clouds.

Signature

Description

moments_points_xldmoments_points_xldMomentsPointsXldMomentsPointsXldMomentsPointsXldmoments_points_xld calculates the moments (M20M20M20M20m20m20, M02M02M02M02m02m02, and M11M11M11M11m11m11) of a point cloud given by a contour or a polygon XLDXLDXLDXLDXLDxld (i.e., the order of the points in the contour or polygon is not taken into account). Therefore, the moments are given by

Here, is the centroid and n the number of points.

If the contour or polygon is closed (end point = start point), the end point of the contour or polygon is not taken into account to avoid that it receives twice the weight of the other points.

moments_points_xldmoments_points_xldMomentsPointsXldMomentsPointsXldMomentsPointsXldmoments_points_xld should be used if the contour XLDXLDXLDXLDXLDxld intersects itself or if it is not possible to close the contour using a line from end to start point without self-intersection, because in this case moments_xldmoments_xldMomentsXldMomentsXldMomentsXldmoments_xld does not produce useful results. To test whether the contours or polygons intersect themselves, test_self_intersection_xldtest_self_intersection_xldTestSelfIntersectionXldTestSelfIntersectionXldTestSelfIntersectionXldtest_self_intersection_xld can be used.

If more than one contour or polygon is passed, the results are stored in tuples in the same order as the respective contours or polygons in XLDXLDXLDXLDXLDxld.

Execution Information

• Multithreading type: reentrant (runs in parallel with non-exclusive operators).
• Multithreading scope: global (may be called from any thread).
• Automatically parallelized on tuple level.

Parameters

Complexity

Let n be the number of points of the contour or polygon. Then the run time is O(n).

Result

moments_points_xldmoments_points_xldMomentsPointsXldMomentsPointsXldMomentsPointsXldmoments_points_xld returns TRUE if the input is not empty. If the input is empty the behavior can be set via set_system(::'no_object_result',<Result>:)set_system("no_object_result",<Result>)SetSystem("no_object_result",<Result>)SetSystem("no_object_result",<Result>)SetSystem("no_object_result",<Result>)set_system("no_object_result",<Result>). If necessary, an exception is raised.

Possible Predecessors

gen_contours_skeleton_xldgen_contours_skeleton_xldGenContoursSkeletonXldGenContoursSkeletonXldGenContoursSkeletonXldgen_contours_skeleton_xld, smooth_contours_xldsmooth_contours_xldSmoothContoursXldSmoothContoursXldSmoothContoursXldsmooth_contours_xld, gen_polygons_xldgen_polygons_xldGenPolygonsXldGenPolygonsXldGenPolygonsXldgen_polygons_xld

Alternatives

moments_xldmoments_xldMomentsXldMomentsXldMomentsXldmoments_xld, moments_any_xldmoments_any_xldMomentsAnyXldMomentsAnyXldMomentsAnyXldmoments_any_xld, moments_any_points_xldmoments_any_points_xldMomentsAnyPointsXldMomentsAnyPointsXldMomentsAnyPointsXldmoments_any_points_xld

See also

moments_any_points_xldmoments_any_points_xldMomentsAnyPointsXldMomentsAnyPointsXldMomentsAnyPointsXldmoments_any_points_xld, area_center_points_xldarea_center_points_xldAreaCenterPointsXldAreaCenterPointsXldAreaCenterPointsXldarea_center_points_xld, moments_region_2ndmoments_region_2ndMomentsRegion2ndMomentsRegion2ndMomentsRegion2ndmoments_region_2nd, area_centerarea_centerAreaCenterAreaCenterAreaCenterarea_center

Module

Foundation