Application of a Fourier-Type Series Approach based on Triangles of Constant Width to Letterforms

Abstract

In this work, we present a novel approach to type design by using Fourier-type series to generate letterforms. We construct a Fourier-type series for functions in $L^2(S^1,\mathbb C)$ based on triangles of constant width instead of circles to model the curves and shapes that define individual characters. In order to compute the coefficients of the series, we construct an isomorphism $\mathcal R:L^2(S^1,\mathbb C)\to L^2(S^1,\mathbb C)$ and study its application to letterforms, thus presenting an alternative to the common use of B\'ezier curves. The proposed method demonstrates potential for creative experimentation in modern type design.