There are a variety of ways to get fabrics to stand like that.
Ideally, buckram* forms would be best, but it's expensive and you'd have to shape it yourself.
You could stiffen your fabric panels with starch and run a single wire down the center of each petal shape, that will get the curve each petal has. I wouldn't bother running wire on the edges, it'll only flatten each panel and the outer edge shape of each petal is smooth and won't need anything special to have that crisp line.
* buckram is that coarse looking stuff that is very rigid inside hats.