moments_xldmoments_xldMomentsXldMomentsXldmoments_xld (Operator)

Name

moments_xldmoments_xldMomentsXldMomentsXldmoments_xld — Geometric moments , , and of contours or polygons.

Signature

Description

moments_xldmoments_xldMomentsXldMomentsXldMomentsXldmoments_xld calculates the moments (M20M20M20M20m20m20, M02M02M02M02m02m02, and M11M11M11M11m11m11) of the region enclosed by the contours or polygons XLDXLDXLDXLDXLDxld. See moments_region_2ndmoments_region_2ndMomentsRegion2ndMomentsRegion2ndMomentsRegion2ndmoments_region_2nd for the definition of these features. The moments are computed by applying Green's theorem using only the points on the contour or polygon, i.e., no region is generated explicitly for the purpose of calculating the features. It is assumed that the contours or polygons are closed. If this is not the case moments_xldmoments_xldMomentsXldMomentsXldMomentsXldmoments_xld will artificially close the contours or polygons.

It should be noted that moments_xldmoments_xldMomentsXldMomentsXldMomentsXldmoments_xld only returns useful results if the contour or polygon encloses a region in the plane. In particular, the contour or polygon must not intersect itself. This is particularly important if open contours or polygons are passed because they are closed automatically, which can produce a self-intersection. To test whether the contours or polygons intersect themselves, test_self_intersection_xldtest_self_intersection_xldTestSelfIntersectionXldTestSelfIntersectionXldTestSelfIntersectionXldtest_self_intersection_xld can be used. If the contour or polygon intersects itself, useful values for the moments can be calculated with moments_points_xldmoments_points_xldMomentsPointsXldMomentsPointsXldMomentsPointsXldmoments_points_xld.

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_xldmoments_xldMomentsXldMomentsXldMomentsXldmoments_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_any_xldmoments_any_xldMomentsAnyXldMomentsAnyXldMomentsAnyXldmoments_any_xld, moments_points_xldmoments_points_xldMomentsPointsXldMomentsPointsXldMomentsPointsXldmoments_points_xld, moments_any_points_xldmoments_any_points_xldMomentsAnyPointsXldMomentsAnyPointsXldMomentsAnyPointsXldmoments_any_points_xld

See also

moments_any_xldmoments_any_xldMomentsAnyXldMomentsAnyXldMomentsAnyXldmoments_any_xld, area_center_xldarea_center_xldAreaCenterXldAreaCenterXldAreaCenterXldarea_center_xld, moments_region_2ndmoments_region_2ndMomentsRegion2ndMomentsRegion2ndMomentsRegion2ndmoments_region_2nd, area_centerarea_centerAreaCenterAreaCenterAreaCenterarea_center

Module

Foundation