2009 Research Summary

Euler Spirals for Font Design

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Carlo H. Séquin and Raph Levien

The search for an aesthetically pleasing, extensible, and robust interpolating spline curve has been going on for several decades. Some fundamental insights have been gained about the characteristics and potential capabilities of two-parameter splines. Among those, a curvature-continuous compound spline constructed from clothoid (Euler spiral) segments has emerged as particularly promising; it closely resembles a minimum-variation curve (MVC) but with a more limited support domain for each segment. A tool kit for the use of these splines in practical applications, such as font design, is under construction.

Figure 1: Font character designed as a compound of clothoid segments (Euler spirals) that are fit together with curvature continuity