# is ellipse inside ellipse in WGS84 ellipsoid

My question is quite clear:

Assume that there is an ellipse, namely EL1. Parameters of the ellipsoid are (focus11 [latitude, longitude], focus12[latitude, longitude], radius1).

And a second ellipse, namely EL2. Which is defined with the same parameter set (focus21 [latitude, longitude], focus22[latitude, longitude], radius2).

The reference ellipsoid is WGS84.

What is the method to find if EL1 contains EL2 ?

So far the best approach I come up with is to convert the EL1 and EL2 to polygons. But it is quite costly.

Is there any idea? Any help is appriciated. Waiting for your replys ...

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I think your parameters for EL1 and EL2 are incomplete. Two foci and a radius don't seem to be enough information to determine and ellipse. Somebody correct me if I'm wrong. – R.K. Dec 25 '12 at 13:03
@r.k. The two focii & radius implicitly give the semi-major & semi-minor axis. Hence the ellipse is fully defined. – Devdatta Tengshe Dec 25 '12 at 13:15
@OP Are you assuming the ellipse is on a flat surface, or is the earth's curveture important in your calculations? – Devdatta Tengshe Dec 25 '12 at 13:18
@DevdattaTengshe I'm a bit confused as to where the radius would be centered at. The foci? If so, aren't two focal radii(with different values) needed? An illustration would be most helpful I think. I hope the OP will reply soon. – R.K. Dec 25 '12 at 13:43
@R.K. Look at this: en.wikipedia.org/wiki/… If you have F1 & F2, and radius (I guess that means a) you can get the center(which is inbetween F1 & F2), and then you can calculate e, and then get the semi-minor axis – Devdatta Tengshe Dec 25 '12 at 15:41