[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-1-en-105":3,"doc-seo-560764-105":53,"doc-detail-560764-en":126},{"code":4,"msg":5,"data":6},0,"success",[7,14,19,24,29,34,39,44,49],{"id":8,"doc_module":9,"doc_module_name":10,"category_name":11,"show_sort_weight":12,"slug":13},11,1,"Template","Presentations",90,"presentations",{"id":15,"doc_module":9,"doc_module_name":10,"category_name":16,"show_sort_weight":17,"slug":18},12,"Resumes",80,"resumes",{"id":20,"doc_module":9,"doc_module_name":10,"category_name":21,"show_sort_weight":22,"slug":23},14,"Invoices",70,"invoices",{"id":25,"doc_module":9,"doc_module_name":10,"category_name":26,"show_sort_weight":27,"slug":28},15,"Posters",60,"posters",{"id":30,"doc_module":9,"doc_module_name":10,"category_name":31,"show_sort_weight":32,"slug":33},16,"Social Media",50,"social-media",{"id":35,"doc_module":9,"doc_module_name":10,"category_name":36,"show_sort_weight":37,"slug":38},17,"Forms",40,"forms",{"id":40,"doc_module":9,"doc_module_name":10,"category_name":41,"show_sort_weight":42,"slug":43},18,"Letters",30,"letters",{"id":45,"doc_module":9,"doc_module_name":10,"category_name":46,"show_sort_weight":47,"slug":48},21,"Paper Templates",5,"papers-templates",{"id":50,"doc_module":9,"doc_module_name":10,"category_name":51,"show_sort_weight":4,"slug":52},158,"General","general-158",{"code":4,"msg":54,"data":55},"ok",{"site_id":56,"language":57,"slug":58,"title":59,"keywords":60,"description":61,"schema_data":62,"social_meta":119,"head_meta":121,"extra_data":123,"updated_unix":125},105,"en","curly-cue-geometric-methods-for-highly-coiled-hair","Curly-Cue - Geometric Methods for Highly Coiled Hair","","Curly-Cue presents geometric algorithms to generate shapes characteristic of highly coiled hair modeled as high-frequency helices. The work identifies three visually relevant phenomena: phase locking, where disparate helices near the scalp form a single curl using a Fourier-based data-driven method; period skipping, where an individual temporarily deviates from the coalesced curl; and switchbacks, or helical perversions, produced via a non-linear optimization that inserts physically valid transitions along a helix. The combined approach yields richly detailed and realistic hair depictions with scalable examples.",{"@graph":63,"@context":118},[64,80,101],{"@type":65,"itemListElement":66},"BreadcrumbList",[67,71,74,77],{"item":68,"name":69,"@type":70,"position":9},"https://docshare.wps.com","Home","ListItem",{"item":72,"name":10,"@type":70,"position":73},"https://docshare.wps.com/template/",2,{"item":75,"name":11,"@type":70,"position":76},"https://docshare.wps.com/template/presentations/",3,{"item":78,"name":59,"@type":70,"position":79},"https://docshare.wps.com/template/curly-cue-geometric-methods-for-highly-coiled-hair/560764/",4,{"url":78,"name":59,"@type":81,"image":82,"author":87,"headline":59,"publisher":90,"fileFormat":93,"inLanguage":57,"description":61,"dateModified":94,"datePublished":95,"encodingFormat":93,"isAccessibleForFree":96,"interactionStatistic":97},"DigitalDocument",{"url":83,"@type":84,"width":85,"height":86},"https://docshare.wps.com/thumbnails/curly-cue-geometric-methods-for-highly-coiled-hair/560764.png","ImageObject",442,249,{"name":88,"@type":89},"Jasmine","Person",{"url":68,"name":91,"@type":92},"DocShare","Organization","application/pdf","2026-10-23","2026-10-12",true,{"@type":98,"interactionType":99,"userInteractionCount":79},"InteractionCounter",{"@type":100},"ViewAction",{"@type":102,"mainEntity":103},"FAQPage",[104,110,114],{"name":105,"@type":106,"acceptedAnswer":107},"What geometric representation underlies the paper’s hair model?","Question",{"text":108,"@type":109},"The paper assumes highly coiled hairs are high-frequency helices as the base primitive, which exposes distinctive geometric phenomena for algorithmic treatment.","Answer",{"name":111,"@type":106,"acceptedAnswer":112},"How does the method for phase locking work?",{"text":113,"@type":109},"It uses a data-driven, Fourier-based approach to compute geometry so disparate helices near the scalp coalesce into a single curl.",{"name":115,"@type":106,"acceptedAnswer":116},"How are switchbacks (helical perversions) generated?",{"text":117,"@type":109},"The paper formulates a non-linear optimization that can insert physically valid switchbacks anywhere along a helix, avoiding reliance on high-resolution physics simulation.","https://schema.org",{"og:url":78,"og:type":120,"og:title":59,"og:site_name":91,"og:description":61},"article",{"robots":122,"canonical":78},"index,follow",{"doc_id":124,"site_id":56},560764,1792588546,{"code":4,"msg":5,"data":127},{"doc_id":124,"user_id":128,"nickname":88,"user_avatar":129,"doc_module":9,"category_id":8,"category_name":11,"doc_title":59,"doc_description":61,"doc_content":130,"file_id":131,"file_url":132,"file_type":133,"file_size":134,"view_count":79,"is_deleted":4,"is_public":9,"is_downloadable":9,"audit_status":9,"page_count":8,"language":135,"language_code":57,"site_id":56,"html_lang":57,"table_of_contents":136,"faqs":137,"seo_title":138,"seo_description":61,"update_tm":139,"read_time":79},2336478487870,"https://ap-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45","Curly-Cue: Geometric Methods for Highly Coiled Hair  \nHAOMIAO WU∗ and ALVIN SHI∗ , Yale University, USA  \nA.M. DARKE, University of California, Santa Cruz, USA THEODORE KIM, Yale University, USA  \nFig. 1. 234K highly coiled hairs generated by combining our phase locking, period skipping, and switchback methods. The head is modelled after New York Times bestselling author Carvell Wallace [Iguodala and Wallace 2019], and used with his permission.  \nWe present geometric methods for generating shapes that are characteristic of highly coiled hair. Different features become visually relevant when hairs are well-approximated by high-frequency helices instead of low-frequency curves, so we present algorithms for three such phenomena. First, a Fourierbased method for phase locking, the process by which disparate helices near the scalp coalesce into a single curl. Second, a method for period skipping which models individual helices deviating from the coalesced curl. Third, anon-linear optimization that directly generates the shapes of switchbacks, a.k.a. helical perversions, which heretofore could only be produced through direct physical simulation. By applying all three methods in tandem, we  \nshow that we can achieve richly detailed depictions of highly coiled hair. CCS Concepts: • Computing methodologies → Shape modeling.  \nAdditional Key Words and Phrases: Hair Modeling, Hairstyling  \n∗Joint first authors  \nAuthors’ Contact Information: Haomiao Wu, [haomiao.wu@yale.edu](haomiao.wu@yale.edu); Alvin Shi, Yale University, USA, [alvin.shi@yale.edu](alvin.shi@yale.edu); A.M. Darke, University of California, Santa Cruz,  \nUSA, [darke@ucsc.edu](darke@ucsc.edu); Theodore Kim, Yale University, USA, [theodore.kim@yale.edu](theodore.kim@yale.edu).  \nPermission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for third-party components of this work must be honored. For all other uses, contact the owner/author(s) .  \nSA Conference Papers ’24, December 3–6, 2024, Tokyo, Japan © 2024 Copyright held by the owner/author(s) .  \nACM ISBN 979-8-4007-1131-2/24/12  \n[https://doi.org/10.1145/3680528.3687641](https://doi.org/10.1145/3680528.3687641)  \nACM Reference Format:  \nHaomiao Wu, Alvin Shi, A.M. Darke, and Theodore Kim. 2024. Curly-Cue: Geometric Methods for Highly Coiled Hair. In SIGGRAPH Asia 2024 Conference Papers (SA Conference Papers ’24), December 3–6, 2024, Tokyo, Japan. ACM, New York, NY, USA, 11 pages. [https://doi.org/10.1145/3680528.3687641](https://doi.org/10.1145/3680528.3687641)  \n1 Introduction  \nHair modeling and simulation has been an active topic in computer graphics research for over three decades [Anjyo et al. 1992] . While many advances have been made, they are usually demonstrated on straight [McAdams et al. 2009], wavy [Kaufman et al. 2014], or loosely curled hair [Iben et al. 2013] . A handful of papers [Bertails et al. 2005; Shi et al. 2023] have dealt with highly coiled, Afro-textured hair, but only one full paper [Patrick et al. 2004] and one short paper [Ogunseitan 2022] has specifically addressed the geometric challenges of modelling this type of hair.  \nIn this paper, we show that when highly coiled hairs, i.e. highfrequency helices, are assumed to be the base primitive, then a variety of challenging geometric phenomena appear that merit further algorithmic investigation.  \nFirst, we examine how a group of disparate hairs coalesce into a single coherent curl as they travel away from the scalp. We call this phenomenon phase locking, borrowing the term’s use in neuroscience [Kolev and Yordanova 1997] to describe multiple wavy signals falling into lock-step. Subsequently, we propose a data-driven, Fourier-based method for computing this geometry to capture the“spongy” texture of highly coiled ha","cbCairzoRzoWRkeN","https://ap.wps.com/l/cbCairzoRzoWRkeN","pdf",66305549,"English","# Introduction\n# Related Works\n## Hair Interpolation","[{\"question\":\"What geometric representation underlies the paper’s hair model?\",\"answer\":\"The paper assumes highly coiled hairs are high-frequency helices as the base primitive, which exposes distinctive geometric phenomena for algorithmic treatment.\"},{\"question\":\"How does the method for phase locking work?\",\"answer\":\"It uses a data-driven, Fourier-based approach to compute geometry so disparate helices near the scalp coalesce into a single curl.\"},{\"question\":\"How are switchbacks (helical perversions) generated?\",\"answer\":\"The paper formulates a non-linear optimization that can insert physically valid switchbacks anywhere along a helix, avoiding reliance on high-resolution physics simulation.\"}]","Curly-Cue - Geometric Methods for Highly Coiled Hair | PDF",1791804078]