Some clarification please. By AN do you mean basically flat components pierce with curvilinear openings or full blown 3-D sculpted forms, and we're not just talking about half rounds on the outside edges of flat curved parts?
Here's an excellent example of one extreme
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here's more on him and his equiptment. The 3-D router machine is pretty amazing - and confounding.
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was also an article in Fine Woodworking perhaps a year or so ago about a guy who makes AN style pieces - that are a little less over the top. His work is more 2-D rounded edges curved parts - can find the specific issue if you really want it.
The style isn't exactly the most efficient use of wood since most of what you start with must be removed because of the curvilinear shapes. Just finding the larger stock to work with may be a problem - and paying for it may put a BIG hole in your wallet. Or you could do a lot of strip glue up to get the basic forms - but making it look like a single piece of wood is not trivial, involving bandsawing and stacking - in order - your thin strips - and THEN making the forms to glue them up on. Steam bending is another skill that you'll probably need, though not all furniture grade woods can be steam bent..
You also need to know how to do "blended" joinery since one part flows into another. And since there are few edges, carving and shaping experience and tools are needed. Again, due to concave and convex surfaces, you'd need to make your own custom scrapers.
To get an idea of ways of doing the blended joinery, find and watch the tape of Sam Maloof's rocking chair construction and Mark Adams'Joinery video
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on how Art Nouveau - y you want to get, you may spend the next ten years of your life learning to make this type of furniture.
Best of luck and post pics as you go - please.
charlie b