Savyth,
I use a heretical system of unframed 1/2-inch BC plywood supported by 1.5-inch PVC pipe. The conventional wisdom is indeed to build solid framing, but I have been happy with my method.
One reason that my scheme works is the rigid attachment of the legs to the table. I drill a 1/2-inch hole through the top of the pipe and put a bolt into it, with two nuts, both inside the pipe, leaving a gap in the middle for the eye of a 1/4-inch eyebolt. The threaded end of the eyebolt comes out of the pipe and through a hole in the table, with a washer and nut on top. Tightening that nut locks the leg into an absolutely firm connection with the table. If you are careful to let only a minimal 1/2 inch of eyebolt protrude, you can easily hide it with some bit of scenery.
I put the legs wherever I need or want them under the free-form table. For some longer spans where a leg is inconvenient, I bolt steel angles to the plywood to stiffen it.
The legs are limber; so this works best for an around-the-walls layout where you can attach or wedge to the walls at a few spots to eliminate swaying. However, I suspect that a couple of sway braces would easily solve the problem for a free-standing layout.