I'm a big fan of the notion that you should never build a guitar that you can't get a case for. Custom cases are expensive, and making your own is a drag. I won't say I always follow this rule, especially cor 'one-off' stuff, but if you're working on something that's intended to be a standard design, it's a good thing to keep in mind. Obviously, since the standard cases are made to fit standard production models, those dimensions are a good place to start. That said, I've never been a fan of the shapes that Martin uses, and some other manufacturers have done things that I'm not keen on copying either. So the thing for me is to come up with a shape that I like that fits the major dimensions of the usual production boxes closely enough to fit the cases. There are several ways to do this.
I've seen layouts, especially for Dreads, that are all straight lines and circular arcs. It works, sort of. I find it boring, but that's just me. In practice you won't end up with that anyway. I've also seen layouts that use a succession of circular arcs. Often the attempt is made to relate them by some simple proportional rule, like the 'Golden Section'. I often find that the closer you adhere to the rule working this way the less I like the shapes, but that's an aesthetic judgement. Given enough circles you can match any curve arbitrarily closely: the trick is to justify all the circles.
Back in the 80s there was an article in the Catgut Society 'Newsletter' about using mathematical curves to draw guitar bodies. Basically, the author was multiplying an egg by a hyperbola to get a waisted shape with a narrower upper bout. Some years later I wrote a BASIC program that allows me to change the parameters of the various equations and look at the resulting shape on the screen. I've added various tweaks over the years when I've needed them to get things like a convincing 'Jumbo' shape, but all of my guitars are designed with this program. I like it because it gives a continuous curve, with no flats or simple circular arcs.
The output of this sort of thing is some sort of cubic spline, more or less, and most vector drawing programs, like 'Illustrator', produce curves this way. With one of these things get pretty simple: you can locate the major points or lines, like the upper and lower bout widths and the waist, on a grid, and connect the dots with curves. The program provides 'handles' you can use to adjust things, and, when you get something you like, you can print it out full size on several sheets of paper.
If you're more traditionally minded you can use a bent stick. An article in the Violin Society journal several years ago showed how you can use this to reproduce the shapes of violins and early guitars (like the Rawlins Strad) quickly. I'm pretty sure you could get a nice looking Dread this way, but not so sanguine about a Torres style Classical. Then again, I haven't tried it. I'll note that some other researchers have been arguing that the major points along the curves can be found using 'Golden Section' layouts, or some variation thereof.
Fred Carlson, who's about the antithesis of 'mathematical', outlined the method he uses in a GAL article some years back. He starts with the strings (which is always a good place to start) and works out from there. He has actually made up a form that has a center line for the strings, marked off at either end where the nut and saddle go, and lines parallel to that indicating the 'usual' waist, upper, and lower bout widths, and the upper and lower limits of the box. These are just useful guidelines, but if you stay more or less within them you'll at least end up with something you can hold on to. Fred comes up with some pretty artistic shapes.
Lots of ways to do it, and they all work for somebody.
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Look at it, and if it's not quite right, erase a line and redraw where it should be. So much easier than all those indirect methods.
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