area_center_xldarea_center_xldAreaCenterXldAreaCenterXldarea_center_xld (Operator)

Name

area_center_xldarea_center_xldAreaCenterXldAreaCenterXldarea_center_xld — Area and center of gravity (centroid) of contours and polygons.

Signature

Description

area_center_xldarea_center_xldAreaCenterXldAreaCenterXldAreaCenterXldarea_center_xld calculates the area and center of gravity (centroid) of the regions enclosed by the contours or polygons XLDXLDXLDXLDXLDxld as well as the order of the points along the boundary. The area and centroid 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. If the points are arranged counterclockwise (i.e., in a positive mathematical sense) in the contour or polygon, PointOrderPointOrderPointOrderPointOrderpointOrderpoint_order will be 'positive'"positive""positive""positive""positive""positive". It is assumed that the contours or polygons are closed. If this is not the case area_center_xldarea_center_xldAreaCenterXldAreaCenterXldAreaCenterXldarea_center_xld will artificially close the contour respectively polygon.

It should be noted that area_center_xldarea_center_xldAreaCenterXldAreaCenterXldAreaCenterXldarea_center_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, a useful value for the center of gravity can be calculated with area_center_points_xldarea_center_points_xldAreaCenterPointsXldAreaCenterPointsXldAreaCenterPointsXldarea_center_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

area_center_xldarea_center_xldAreaCenterXldAreaCenterXldAreaCenterXldarea_center_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

area_center_points_xldarea_center_points_xldAreaCenterPointsXldAreaCenterPointsXldAreaCenterPointsXldarea_center_points_xld

See also

moments_xldmoments_xldMomentsXldMomentsXldMomentsXldmoments_xld, moments_any_xldmoments_any_xldMomentsAnyXldMomentsAnyXldMomentsAnyXldmoments_any_xld, area_centerarea_centerAreaCenterAreaCenterAreaCenterarea_center, moments_region_2ndmoments_region_2ndMomentsRegion2ndMomentsRegion2ndMomentsRegion2ndmoments_region_2nd

Module

Foundation