> Breaking at the dateline doesn't make any difference.
> See:http://www.champlindesign.com/maps/largeOverlay/largeOverlayTest2.html.

But
     var sw1 = new google.maps.LatLng(-32.91,82.96);
     var ne1 = new google.maps.LatLng(71.1,-180);
doesn't make sense ; you are asking the API to see 82.96 as being more
westerly than -180 (which is as far "west" as you can get).  I'd use
180, logically the same longitude I know, but not ambiguous about
which way round to go.

May well not fix your problems though !

    var sw2 = new google.maps.LatLng(-32.91,-180) ;
    var ne2 = new google.maps.LatLng(71.1,37.38) ;
This chunk is still bigger than a hemisphere's worth, which I reckon
is what is causing the odd effects.

> Is there a way to get large non-tiled overlays to stay put and not
> jump hemispheres?

There were ways to inhibit wrapping in v2, dunno about v3.

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