hmm yes a 180 degree full fisheye should manage very well. Bit expensive for only a 1 off project.
You would need to set the camera/tripod up in the center of the people ring. Give your self about 2 feet distance walking room around the tripod base. You would need to have the people ring in as close as you can without too much crowding. 10 foott diameter circle probably it too far away. Try 6 to 8 feet.
When you take the images, pre advise the group to freeze action. Slightest movement, tickling of noses etc will blur the people. Take your imaging. Give it a rest.
Take 2 or 3 more panoramas while your at it... ALWAYS starting a the FIRST CLICK stop.
Do not take the second round of images at the last click stop from last panorama.
So if you are taking 4 images.... at 90 degrees.... clickstop 1 at 0, 2 at 90, 3 at 180, 4 at 270 degrees. NOW CLICK 1 more space to return to the 0 zero position.
What this will do for you is allow you to swap out image #1 between panorama sets in the event you get every one correct.. eyes open, hair straightened.... no blinking in shots 2, 3, 4 in panorama 1... and there is a better #1 shot in panorama #3.. you can just substitute it in the stitch series.
If you don't return to click stop 1 (5th click)... your background will be out of sync in each panorama.
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EasyPano - Panoweaver