Hey, Matt!
Cool ground plan! I love that you're rocking an off-center look!
As everyone has said, you have options. For me, it's always about how little I can spend compared to how far away the audience is. If I can get away with cardboard, knowing that I may have to add a treatment to interrupt the way cardboard paints up, then that's probably the cheapest.
However, I use 1/8" masonite for things that need to hold up a bit better; you'll need to plan your seams so they hit supported, less curvey bits.
There are also times I use fabrics or a mylar fringe curtain. It just depends on the look and budget.
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Joselyn Ludtke
Technical Theatre Instructor
Auburn Creative and Performing Arts High School
IL
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