{"title":"基于恒定宽度三角形的傅立叶级数方法在字母字体中的应用","authors":"Micha Wasem, Florence Yerly","doi":"arxiv-2409.11958","DOIUrl":null,"url":null,"abstract":"In this work, we present a novel approach to type design by using\nFourier-type series to generate letterforms. We construct a Fourier-type series\nfor functions in $L^2(S^1,\\mathbb C)$ based on triangles of constant width\ninstead of circles to model the curves and shapes that define individual\ncharacters. In order to compute the coefficients of the series, we construct an\nisomorphism $\\mathcal R:L^2(S^1,\\mathbb C)\\to L^2(S^1,\\mathbb C)$ and study its\napplication to letterforms, thus presenting an alternative to the common use of\nB\\'ezier curves. The proposed method demonstrates potential for creative\nexperimentation in modern type design.","PeriodicalId":501162,"journal":{"name":"arXiv - MATH - Numerical Analysis","volume":"43 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Application of a Fourier-Type Series Approach based on Triangles of Constant Width to Letterforms\",\"authors\":\"Micha Wasem, Florence Yerly\",\"doi\":\"arxiv-2409.11958\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this work, we present a novel approach to type design by using\\nFourier-type series to generate letterforms. We construct a Fourier-type series\\nfor functions in $L^2(S^1,\\\\mathbb C)$ based on triangles of constant width\\ninstead of circles to model the curves and shapes that define individual\\ncharacters. In order to compute the coefficients of the series, we construct an\\nisomorphism $\\\\mathcal R:L^2(S^1,\\\\mathbb C)\\\\to L^2(S^1,\\\\mathbb C)$ and study its\\napplication to letterforms, thus presenting an alternative to the common use of\\nB\\\\'ezier curves. The proposed method demonstrates potential for creative\\nexperimentation in modern type design.\",\"PeriodicalId\":501162,\"journal\":{\"name\":\"arXiv - MATH - Numerical Analysis\",\"volume\":\"43 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Numerical Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.11958\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Numerical Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.11958","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Application of a Fourier-Type Series Approach based on Triangles of Constant Width to Letterforms
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.