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Manually designing foundation paper pieceable patterns that meet all of these constraints is challenging. In this work we mathematically formalize the foundation paper piecing process and use this formalization to develop an algorithm that can automatically check if an input pattern geometry is foundation paper pieceable. Our key insight is that we can represent the geometric pattern design using a certain type of\n            <jats:italic>dual hypergraph<\/jats:italic>\n            where nodes represent faces and hyperedges represent\n            <jats:italic>seams<\/jats:italic>\n            connecting two or more nodes. We show that determining whether the pattern is paper pieceable is equivalent to checking whether this hypergraph is acyclic, and if it is acyclic, we can apply a\n            <jats:italic>leaf-plucking<\/jats:italic>\n            algorithm to the hypergraph to generate viable sewing orders for the pattern geometry. We implement this algorithm in a design tool that allows quilt designers to focus on producing the geometric design of their pattern and let the tool handle the tedious task of determining whether the pattern is foundation paper pieceable.\n          <\/jats:p>","DOI":"10.1145\/3450626.3459853","type":"journal-article","created":{"date-parts":[[2021,7,20]],"date-time":"2021-07-20T00:04:26Z","timestamp":1626739466000},"page":"1-14","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":17,"title":["A mathematical foundation for foundation paper pieceable quilts"],"prefix":"10.1145","volume":"40","author":[{"given":"Mackenzie","family":"Leake","sequence":"first","affiliation":[{"name":"Stanford University"}]},{"given":"Gilbert","family":"Bernstein","sequence":"additional","affiliation":[{"name":"UC Berkeley"}]},{"given":"Abe","family":"Davis","sequence":"additional","affiliation":[{"name":"Cornell University"}]},{"given":"Maneesh","family":"Agrawala","sequence":"additional","affiliation":[{"name":"Stanford University"}]}],"member":"320","published-online":{"date-parts":[[2021,7,19]]},"reference":[{"key":"e_1_2_2_1_1","unstructured":"Ingrid Alteneder. 2020. Adorable Animal Quilting. Page Street.  Ingrid Alteneder. 2020. Adorable Animal Quilting. Page Street."},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/2897824.2925896"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/2461912.2461975"},{"key":"e_1_2_2_4_1","volume-title":"State of the Art on Stylized Fabrication. Computer Graphics Forum 37","author":"Bickel Bernd","year":"2018","unstructured":"Bernd Bickel , Paolo Cignoni , Luigi Malomo , and Nico Pietroni . 2018. State of the Art on Stylized Fabrication. Computer Graphics Forum 37 ( 2018 ). http:\/\/vcg.isti.cnr.it\/Publications\/2018\/BCMP18 Bernd Bickel, Paolo Cignoni, Luigi Malomo, and Nico Pietroni. 2018. State of the Art on Stylized Fabrication. 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In SBM. 165--174."},{"key":"e_1_2_2_8_1","unstructured":"Arnout Cosman. 2012. Quilt Assistant v2.24. https:\/\/quiltassistant.com\/  Arnout Cosman. 2012. Quilt Assistant v2.24. https:\/\/quiltassistant.com\/"},{"key":"e_1_2_2_9_1","doi-asserted-by":"crossref","unstructured":"Erik D Demaine and Martin L Demaine. 2002. Recent results in computational origami. In Origami3: Third International Meeting of Origami Science Mathematics and Education. 3--16.  Erik D Demaine and Martin L Demaine. 2002. Recent results in computational origami. In Origami3: Third International Meeting of Origami Science Mathematics and Education. 3--16.","DOI":"10.1201\/b15735-3"},{"key":"e_1_2_2_10_1","unstructured":"Phoebe Moon Designs. 2020. The seven deadly sins of foundation paper piecing. https:\/\/phoebemoon.com\/tutorials\/paper-piecing.htm  Phoebe Moon Designs. 2020. 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Yohsuke Furuta Nobuyuki Umetani Jun Mitani Takeo Igarashi and Yukio Fukui. 2010. A Film Balloon Design System Integrated with Shell Element Simulation.. In Eurographics (Short Papers). 33--36."},{"key":"e_1_2_2_16_1","doi-asserted-by":"publisher","DOI":"10.1145\/2601097.2601106"},{"key":"e_1_2_2_17_1","unstructured":"Hayley Grzych. 2018. Beginner-friendly foundation paper piecing. https:\/\/weallsew.com\/beginner-friendly-foundation-paper-piecing  Hayley Grzych. 2018. Beginner-friendly foundation paper piecing. https:\/\/weallsew.com\/beginner-friendly-foundation-paper-piecing"},{"key":"e_1_2_2_18_1","doi-asserted-by":"publisher","DOI":"10.1145\/2816795.2818118"},{"key":"e_1_2_2_19_1","doi-asserted-by":"publisher","DOI":"10.1145\/571985.571999"},{"key":"e_1_2_2_20_1","doi-asserted-by":"publisher","DOI":"10.1109\/MCG.2010.74"},{"key":"e_1_2_2_21_1","doi-asserted-by":"publisher","DOI":"10.1145\/2787626.2792601"},{"key":"e_1_2_2_22_1","unstructured":"Sylvia Kaptein. 2020. 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