First off I'm no mathmatician (did I spell that right?) I am a timber framer though and I would loft it out on a floor. full size and I would try to find curved logs and slab them (with a chainsawn mill) for the curved components.The easiest way , for me , would be to cut and fit the main bent , square , secure , and then piece on piece the remaining parts. I would have a solid build plan on paper before I order any wood. Find a large smooth area , preferably indoors and lay out your design with chalk. If this doesn't help to figure out the math it may give you a better feel for your design so you'll be confident enough in understanding how to build it anyway.