Application of a Fourier-Type Series Approach based on Triangles of Constant Width to Letterforms
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909010727272448 |
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| author | Wasem, Micha Yerly, Florence |
| author_facet | Wasem, Micha Yerly, Florence |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_11958 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Application of a Fourier-Type Series Approach based on Triangles of Constant Width to Letterforms Wasem, Micha Yerly, Florence Classical Analysis and ODEs Numerical Analysis Functional Analysis 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. |
| title | Application of a Fourier-Type Series Approach based on Triangles of Constant Width to Letterforms |
| topic | Classical Analysis and ODEs Numerical Analysis Functional Analysis |
| url | https://arxiv.org/abs/2409.11958 |