elliptic_axis_points_xldelliptic_axis_points_xldEllipticAxisPointsXldelliptic_axis_points_xldEllipticAxisPointsXldEllipticAxisPointsXld (Operator)

Name

elliptic_axis_points_xldelliptic_axis_points_xldEllipticAxisPointsXldelliptic_axis_points_xldEllipticAxisPointsXldEllipticAxisPointsXld — Parameters of the equivalent ellipse of contours or polygons treated as point clouds.

Signature

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

Description

The operator elliptic_axis_points_xldelliptic_axis_points_xldEllipticAxisPointsXldelliptic_axis_points_xldEllipticAxisPointsXldEllipticAxisPointsXld calculates the radii (RaRaRaRaRara, RbRbRbRbRbrb) and the orientation (PhiPhiPhiPhiPhiphi, in radians) of the ellipse having the same orientation and the same aspect ratio as the point cloud given by the contour or polygon XLDXLDXLDXLDXLDXLD (i.e., the order of the points in the contour or polygon is not taken into account). 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.

Calculation:

        If the moments M20, M02 and M11 are
        normalized to the area (see moments_points_xldmoments_points_xldMomentsPointsXldmoments_points_xldMomentsPointsXldMomentsPointsXld),
        the major radius RaRaRaRaRara and minor radius RbRbRbRbRbrb are
        calculated as:

        RaRaRaRaRara = sqrt(8.0*(M20+M02+sqrt((M20-M02)^2+4.0*M11^2)))/2.0
        RbRbRbRbRbrb = sqrt(8.0*(M20+M02-sqrt((M20-M02)^2+4.0*M11^2)))/2.0

        The orientation PhiPhiPhiPhiPhiphi, i.e., the angle between the major axis
        and the x (column) axis, is defined by:

        PhiPhiPhiPhiPhiphi = -0.5 * atan2(2.0 * M11,M02 - M20)

elliptic_axis_points_xldelliptic_axis_points_xldEllipticAxisPointsXldelliptic_axis_points_xldEllipticAxisPointsXldEllipticAxisPointsXld should be used if the contour XLDXLDXLDXLDXLDXLD 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 elliptic_axis_xldelliptic_axis_xldEllipticAxisXldelliptic_axis_xldEllipticAxisXldEllipticAxisXld does not produce useful results. To test whether the contours or polygons intersect themselves, test_self_intersection_xldtest_self_intersection_xldTestSelfIntersectionXldtest_self_intersection_xldTestSelfIntersectionXldTestSelfIntersectionXld 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 XLDXLDXLDXLDXLDXLD.