Bending and deforming a two-dimensional mesh with constant surface area

I want to be able to create a two-dimensional mesh representing a flower petal and then to bend, twist and deform a number of instances of the original in such a way that the original surface area is retained.

To put it another way, if I were to flatten out one of the deformed petals so that it was planar once again, I’d want it to be the same shape I started out with.

Surely this is possible - but I can’t work out how to do it

lattice modifier/mesh deform modifier!

any doc on this constant area thing for lattice or mesh deform ?

thanks

I thought that might be the direction. I need to get up to speed with that stuff.
Thanks

If you would need say projection on XY plane stay the same you could add one vertex loop around and hide that before using proportional or other deforms. If you do not do extremes that would give you some idea what goes where after you unhide verts. Delete them when done.

If you scale lattice elements your object’s area will not stay the same.