area_center_points_xld — Area and center of gravity (centroid) of contours and polygons
treated as point clouds.
area_center_points_xld calculates the area and center of
gravity (centroid) of the point clouds given by contours or polygons
XLD (i.e., the order of the points in the contour or
polygon is not taken into account). The area corresponds to the
number of points in the point cloud. The centroid is given by the
arithmetic mean of all 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.
area_center_points_xld should be used if the contour
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
area_center_xld does not produce useful results. To test whether the
contours or polygons intersect themselves,
test_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
Even if the contour or polygon
XLD is not intersecting itself, the
area_center_points_xld significantly differs from the
area_center_xld as it is calculated from the point cloud
and not from the enclosed region.
Point clouds to be examined in form of contours or polygons.
Area of the point cloud.
Row coordinate of the centroid.
Column coordinate of the centroid.
Let n be the number of points of the contour or polygon. Then the run time is O(n).
area_center_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>:). If necessary,
an exception is raised.