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#### 7.1.10 `2d_ellipse`: Cartesian Matching of Elliptical Regions

    matcher=2d_ellipse values*='<x> <y> <primary-radius> <secondary-radius>
                                <orientation-angle/deg>'
                       params='<scale>'
                       tuning='<bin-factor>'

> `values*`:
>   - `x`: X coordinate of centre
>   - `y`: Y coordinate of centre
>   - `primary-radius`: Length of ellipse semi-major axis
>   - `secondary-radius`: Length of ellipse semi-minor axis
>   - `orientation-angle/deg`: Angle from X axis towards Y axis of semi-major axis
> `params`:
>   - `scale`: Rough average of per-object error distance; just used for tuning in conjunction with bin factor
> `tuning`:
>   - `bin-factor`: Scaling factor to adjust bin size; larger values mean larger bins

The `2d_ellipse` matcher compares elliptical regions in a 2d plane for overlap. Each row has to specify five values, giving the centre, the major and minor radii, and the orientation angle of an ellipse. Rows are considered to match if there is any overlap between the ellipses. The goodness of match is a normalised generalisation of the symmetrical case used by the isotropic matcher, in which the best possible match is two concentric ellipses, and the worst allowable match is when the circumferences just touch.

Note the orientation angle is measured anticlockwise from the horizontal, unlike the position angle used by the `skyellipse` matcher.

The `scale` parameter must be supplied, and should be approximately the characteristic size of the per-object major radius. In conjunction with the `bin-factor` tuning parameter its value affects the performance of the match, but not the result.

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STILTS - Starlink Tables Infrastructure Library Tool Set
Starlink User Note256
STILTS web page: http://www.starlink.ac.uk/stilts/
Author email: m.b.taylor@bristol.ac.uk
Mailing list: topcat-user@jiscmail.ac.uk