Creating 'planar' surface on 3d plane

 From:  GuyLuke
11156.5 
Thank you for the solutions. Just wondering why the planar command can't be made to render nonplanar surfaces like this from a closed curve? I'm also trying to figure out how to cut the 3d closed curve into equal halves, I would have thought a boolean merge with a straight line through the middle would have worked but it doesn't.

EDITED: 23 Jul 2023 by GUYLUKE