elliptic_axis_xldelliptic_axis_xldEllipticAxisXldelliptic_axis_xldEllipticAxisXldEllipticAxisXld (Operator)

Name

elliptic_axis_xldelliptic_axis_xldEllipticAxisXldelliptic_axis_xldEllipticAxisXldEllipticAxisXld — Parameters of the equivalent ellipse of contours or polygons.

Signature

elliptic_axis_xld(XLD : : : Ra, Rb, Phi)

The operator elliptic_axis_xldelliptic_axis_xldEllipticAxisXldelliptic_axis_xldEllipticAxisXldEllipticAxisXld calculates the radii and the orientations of the ellipses having the same orientation and the same aspect ratio as the input contours or polygons. The length of the major radius RaRaRaRaRara and the minor radius RbRbRbRbRbrb as well as the orientation of the main axis with regard to the horizontal (PhiPhiPhiPhiPhiphi) are determined. The angle is indicated in radians. It is assumed that the contours or polygons are closed. If this is not the case area_center_xldarea_center_xldAreaCenterXldarea_center_xldAreaCenterXldAreaCenterXld will artificially close the contours or polygons.

Calculation: If the moments , and are normalized and passed to the area (see moments_xldmoments_xldMomentsXldmoments_xldMomentsXldMomentsXld), the radii RaRaRaRaRara and RbRbRbRbRbrb are calculated as:

The orientation PhiPhiPhiPhiPhiphi is defined by:

It should be noted that elliptic_axis_xldelliptic_axis_xldEllipticAxisXldelliptic_axis_xldEllipticAxisXldEllipticAxisXld 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_xldTestSelfIntersectionXldtest_self_intersection_xldTestSelfIntersectionXldTestSelfIntersectionXld can be used. If the contour or polygon intersects itself, useful values for the ellipse parameters can be calculated with elliptic_axis_points_xldelliptic_axis_points_xldEllipticAxisPointsXldelliptic_axis_points_xldEllipticAxisPointsXldEllipticAxisPointsXld.

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.