I've always assumed that the vector outlines contained in a font file are essentially mathematical formulas describing each of those shapes; and that no matter how similar two fonts might appear, the combination of characteristics (proportions, contours, angles, spacing, etc) results in a vector equation revealing more differences than the eye might be able to decipher. I don't know how accurate this is, but as I am familiar with the concept of vectors in algebra, it seems that it should at least be possible to tell if a given font was produced by altering the outlines of a paid font whose EULA forbade such alterations.
Now that live typographic interpolation and parametric fonts are being used in web browsers, and foundries are able to create enormous font families extrapolated from as little as one master, I wonder how difficult it will become to tell original work from derivative work. By derivative I mean originating from the same digital source.
My becoming a typographer was born of a need for a typeface for projects when nothing in existence seemed to fit. So I am asking as an artist, out of curiosity ... not as a crybaby complaining that someone stole my shapes, er, intellectual property. Plagiarism offends me more than capitalism or piracy combined, because of the sheer lack of imagination.
So my question has two parts:
What methods exist for determining the similarity or difference of fonts?
How do they function? Specifically, can they measure both qualitative and quantitative changes to the original's outlines? Some seem to assume that making a font slightly heavier means the outlines are unique, but as math based shapes, I would expect that the bulk of the equation is proportionally identical, even if the glyphs have grown along one axis.