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In the history of type design, two methods have been used to scale type-- to produce enlarged or reduced letterforms from a reference size. With original handcut fonts, designers performed optical scaling (scaling by eye) that varied the proportions of letterform features over a range of sizes in a nonlinear manner. That is, letterform feature proportions were size dependent. This was an entirely manual and intuitive process. More recently, however, the use of the lens, as well as computational and other technologies, has allowed letterforms to be scaled automatically from a reference character, a simple proportional enlargement or reduction. To date, little work has been done to combine these two methods, that is to say, to automatically perform nonlinear scaling of a reference character in order to approximate the optical scaling performed by skilled type designers and punchcutters. This research developed a mathematical model of optical scale in type design, consisting of two parts: (1) a model of the scaling of individual letterform features; and (2) a model of the scaling of entire letterforms. The model was tested by applying it to the original handcut fonts that supplied the initial data for the research in order to generate synthetic letterforms. These nonlinear synthetic letterforms were then compared with the originals, as well with proportionally scaled letterforms generated by the model approximated the original optically scaled handcut letterforms. In addition, the performance of the proportionally scaled letterforms was compared with the originals, as well as with the nonlinear, synthetic forms.

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