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

TL;DR

This paper introduces a new Fourier-type series method based on triangles of constant width for generating letterforms, offering an alternative to traditional curve modeling in type design.

Contribution

It presents a novel Fourier series construction using triangles of constant width, expanding tools for creative and computational type design.

Findings

The method effectively models letterforms with Fourier series based on triangles.

It provides an alternative to Bézier curves for curve representation in type design.

Potential for enhanced creative experimentation in digital typography.

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.