One of my favorite chair designs is Eames LCW molded plywood lounge chair. It's a design classic; the fine detailed surfacing work is incredible and super comfortable. It has been a source of inspiration for quite a lot of my furniture and in this case while using a completely different technology I was able to resemble his masterpiece.
CNC Furniture has been for a few years already but hasn't really taken off. I believe this is because designers haven't spend enough time designing with that technology in mind. Most of the CNC furniture I found online have the typical joinery exposed or have a rigid feel. I played around with the ShopBot Buddy (worktable 4' x 2') and made a family of chairs: Dining Chair, Stool and this Lounge Chair. CNC Routers have become affordable in the last couple of years and there are quite a lot of DIY CNC Routers out there. If you have a TechShop close by you can probably make it over there.