Application of a Fourier-Type Series Approach based on Triangles of Constant Width to Letterforms
For type designers, this work presents a novel mathematical framework for creative letterform generation, but it is preliminary and lacks empirical validation.
The paper introduces a Fourier-type series based on triangles of constant width to generate letterforms, offering an alternative to Bézier curves for type design. No concrete performance numbers are provided.
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 Bézier curves. The proposed method demonstrates potential for creative experimentation in modern type design.