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

area_center_xld calculates the area and center of gravity (centroid) of the regions enclosed by the contours or polygons XLD 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, PointOrder will be 'positive'. It is assumed that the contours or polygons are closed. If this is not the case area_center_xld will artificially close the contour respectively polygon.

It should be noted that area_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_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_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 XLD.

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

area_center_xld returns 2 (H_MSG_TRUE) if the input is not empty. If the input is empty the behavior can be set via set_system(::'no_object_result',<Result>:). If necessary, an exception is raised.

area_center_xld is reentrant and automatically parallelized (on tuple level).

gen_contours_skeleton_xld, smooth_contours_xld, gen_polygons_xld

area_center_points_xld

moments_xld, moments_any_xld, area_center, moments_region_2nd

Foundation