{"type": "body", "content": "", "style": "font-family: Helvetica, Arial, sans-serif; font-weight: 300", "bbox": [8, 21, 1264, 1320], "children": [{"type": "div", "content": "", "style": "margin: 0 auto; width: 70%; color: #2a2a2a", "bbox": [197, 21, 884, 1280], "children": [{"type": "div", "content": "", "style": null, "bbox": [197, 21, 884, 74], "children": [{"type": "h1", "content": "A Mathematical Foundation for Foundation Paper Pieceable Quilts", "style": "text-align: center; font-weight: 300", "bbox": [197, 21, 884, 74], "children": []}]}, {"type": "div", "content": "", "style": "text-align: center; font-weight: 300; width: 100%; margin: 5px auto", "bbox": [197, 116, 884, 61], "children": [{"type": "ul", "content": "", "style": "list-style-type: none; margin: 0 auto; padding: 0; overflow: hidden; font-size: 14pt", "bbox": [197, 116, 884, 26], "children": [{"type": "li", "content": "", "style": "display: inline-block; margin: 0 20px", "bbox": [282, 116, 158, 26], "children": [{"type": "sup", "content": "\u273b", "style": null, "bbox": [427, 116, 13, 17], "children": []}]}, {"type": "li", "content": "", "style": "display: inline-block; margin: 0 20px", "bbox": [485, 116, 151, 26], "children": [{"type": "sup", "content": "\u2727", "style": null, "bbox": [624, 116, 13, 17], "children": []}]}, {"type": "li", "content": "", "style": "display: inline-block; margin: 0 20px", "bbox": [682, 116, 98, 26], "children": [{"type": "sup", "content": "\u2731", "style": null, "bbox": [767, 116, 13, 17], "children": []}]}, {"type": "li", "content": "", "style": "display: inline-block; margin: 0 20px", "bbox": [826, 116, 171, 26], "children": [{"type": "sup", "content": "\u273b", "style": null, "bbox": [984, 116, 13, 17], "children": []}]}]}, {"type": "p", "content": "\u273b Stanford University, \u2727 UC Berkeley, \u2731 Cornell University", "style": null, "bbox": [197, 159, 884, 19], "children": []}]}, {"type": "div", "content": "", "style": "height: 15%; margin: 0 auto; text-align: center", "bbox": [197, 194, 884, 18], "children": []}, {"type": "div", "content": "Three foundation paper pieced designs generated in our tool and sewn in colorful fabrics", "style": "text-align: center", "bbox": [197, 212, 884, 18], "children": []}, {"type": "hr", "content": "", "style": null, "bbox": [197, 238, 884, 2], "children": []}, {"type": "div", "content": "", "style": "margin: 10px 0", "bbox": [197, 250, 884, 202], "children": [{"type": "span", "content": "Abstract:", "style": "font-weight: 500; color: #000; font-size: 14pt", "bbox": [197, 250, 73, 21], "children": []}]}, {"type": "hr", "content": "", "style": null, "bbox": [197, 462, 884, 2], "children": []}, {"type": "div", "content": "", "style": null, "bbox": [197, 472, 884, 18], "children": [{"type": "span", "content": "Overview:", "style": "font-weight: 500; color: #000", "bbox": [197, 472, 71, 17], "children": []}]}, {"type": "div", "content": "", "style": null, "bbox": [197, 490, 884, 18], "children": []}, {"type": "div", "content": "", "style": null, "bbox": [197, 508, 884, 144], "children": [{"type": "span", "content": "Fig. 1:", "style": "font-weight: 500; color: #000", "bbox": [197, 508, 44, 17], "children": []}]}, {"type": "hr", "content": "", "style": null, "bbox": [197, 660, 884, 2], "children": []}, {"type": "div", "content": "", "style": null, "bbox": [197, 670, 884, 166], "children": [{"type": "span", "content": "Videos:", "style": "font-weight: 500; color: #000", "bbox": [197, 670, 53, 17], "children": []}, {"type": "ul", "content": "", "style": "list-style-type: none; padding-left: 0", "bbox": [197, 704, 884, 132], "children": [{"type": "li", "content": "", "style": "margin-bottom: 20px", "bbox": [197, 704, 884, 18], "children": [{"type": "a", "content": "SIGGRAPH'21 long talk", "style": "font-weight: 500; color: #06f; text-decoration: none", "bbox": [197, 704, 169, 17], "children": []}]}, {"type": "li", "content": "", "style": "margin-bottom: 20px", "bbox": [197, 742, 884, 18], "children": [{"type": "a", "content": "SIGGRAPH'21 short talk", "style": "font-weight: 500; color: #06f; text-decoration: none", "bbox": [197, 742, 174, 17], "children": []}]}, {"type": "li", "content": "", "style": "margin-bottom: 20px", "bbox": [197, 780, 884, 18], "children": [{"type": "a", "content": "SIGGRAPH'21 fast forward", "style": "font-weight: 500; color: #06f; text-decoration: none", "bbox": [197, 780, 193, 17], "children": []}]}, {"type": "li", "content": "", "style": "margin-bottom: 20px", "bbox": [197, 818, 884, 18], "children": [{"type": "a", "content": "Paper overview", "style": "font-weight: 500; color: #06f; text-decoration: none", "bbox": [197, 818, 110, 17], "children": []}]}]}]}, {"type": "hr", "content": "", "style": null, "bbox": [197, 856, 884, 2], "children": []}, {"type": "div", "content": "", "style": null, "bbox": [197, 866, 884, 166], "children": [{"type": "span", "content": "Paper & Supplemental materials:", "style": "font-weight: 500; color: #000", "bbox": [197, 866, 233, 17], "children": []}, {"type": "ul", "content": "", "style": "list-style-type: none; padding-left: 0", "bbox": [197, 900, 884, 132], "children": [{"type": "li", "content": "", "style": "margin-bottom: 20px", "bbox": [197, 900, 884, 18], "children": [{"type": "a", "content": "Paper PDF", "style": "font-weight: 500; color: #06f; text-decoration: none", "bbox": [197, 900, 79, 17], "children": []}]}, {"type": "li", "content": "", "style": "margin-bottom: 20px", "bbox": [197, 938, 884, 18], "children": [{"type": "a", "content": "Supplemental pattern images (50 designs and hypergraphs)", "style": "font-weight: 500; color: #06f; text-decoration: none", "bbox": [197, 938, 429, 17], "children": []}]}, {"type": "li", "content": "", "style": "margin-bottom: 20px", "bbox": [197, 976, 884, 18], "children": [{"type": "a", "content": "Try our tool!", "style": "font-weight: 500; color: #06f; text-decoration: none", "bbox": [197, 976, 89, 17], "children": []}]}, {"type": "li", "content": "", "style": "margin-bottom: 20px", "bbox": [197, 1014, 884, 18], "children": [{"type": "a", "content": "Code", "style": "font-weight: 500; color: #06f; text-decoration: none", "bbox": [197, 1014, 42, 17], "children": []}]}]}]}, {"type": "hr", "content": "", "style": null, "bbox": [197, 1052, 884, 2], "children": []}, {"type": "div", "content": "", "style": null, "bbox": [197, 1062, 884, 128], "children": [{"type": "span", "content": "News articles:", "style": "font-weight: 500; color: #000", "bbox": [197, 1062, 99, 17], "children": []}, {"type": "ul", "content": "", "style": "list-style-type: none; padding-left: 0", "bbox": [197, 1096, 884, 94], "children": [{"type": "li", "content": "", "style": "margin-bottom: 20px", "bbox": [197, 1096, 884, 18], "children": [{"type": "a", "content": "Stanford News", "style": "font-weight: 500; color: #06f; text-decoration: none", "bbox": [197, 1096, 104, 17], "children": []}]}, {"type": "li", "content": "", "style": "margin-bottom: 20px", "bbox": [197, 1134, 884, 18], "children": [{"type": "a", "content": "Stanford Daily", "style": "font-weight: 500; color: #06f; text-decoration: none", "bbox": [197, 1134, 100, 17], "children": []}]}, {"type": "li", "content": "", "style": "margin-bottom: 20px", "bbox": [197, 1172, 884, 18], "children": [{"type": "a", "content": "The Quilt Show Blog", "style": "font-weight: 500; color: #06f; text-decoration: none", "bbox": [197, 1172, 145, 17], "children": []}]}]}]}, {"type": "hr", "content": "", "style": null, "bbox": [197, 1210, 884, 2], "children": []}, {"type": "div", "content": "", "style": null, "bbox": [197, 1228, 884, 74], "children": [{"type": "ul", "content": "", "style": "list-style-type: none; padding-left: 0", "bbox": [197, 1228, 884, 74], "children": [{"type": "li", "content": "", "style": "margin-bottom: 20px", "bbox": [197, 1228, 884, 36], "children": [{"type": "a", "content": "webpage", "style": "font-weight: 500; color: #06f; text-decoration: none", "bbox": [723, 1228, 64, 17], "children": []}]}, {"type": "li", "content": "", "style": "margin-bottom: 20px", "bbox": [197, 1284, 884, 18], "children": [{"type": "span", "content": "Questions?", "style": "font-weight: 500; color: #000", "bbox": [197, 1284, 85, 17], "children": []}, {"type": "a", "content": "fppresearch2021@gmail.com", "style": "text-decoration: none", "bbox": [425, 1284, 209, 17], "children": []}]}]}]}]}, {"type": "footer", "content": "", "style": "text-align: center; padding: 10px", "bbox": [8, 1322, 1264, 20], "children": []}]}
<!DOCTYPE html>

<html><head></head><body><div id="container"><div id="title"><h1>A Mathematical Foundation for Foundation Paper Pieceable Quilts</h1></div><div id="authors"><ul><li>Mackenzie Leake<sup>✻</sup></li><li>Gilbert Bernstein<sup>✧</sup></li><li>Abe Davis<sup>✱</sup></li><li>Maneesh Agrawala<sup>✻</sup></li></ul><p>✻ Stanford University, ✧ UC Berkeley, ✱ Cornell University</p></div><div class="row"><img class="topimage" src="images/cactus.png" style="width:auto;max-height: 200px"/><img class="topimage" src="images/camera_small.png" style="width:auto;max-height: 200px"/><img class="topimage" src="images/house.png" style="width:auto;max-height: 200px"/></div><div id="top-caption">
				Three foundation paper pieced designs generated in our tool and sewn in colorful fabrics
            </div><hr/><div id="abstract"><span class="keyword">Abstract:</span> 
                Foundation paper piecing is a popular technique for constructing fabric
				patchwork quilts using printed paper patterns. But, the construction process
				imposes constraints on the geometry of the pattern and the order in which
				the fabric pieces are attached to the quilt. 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 dual hypergraph where nodes represent faces and hyperedges
				represent seams 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 leaf-plucking
				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
				lets the tool handle the tedious task of determining whether the pattern is
				foundation paper pieceable.
                <span></span></div><hr/><div id="overview"><span class="keyword">Overview:</span></div><div id="teaser"><img src="images/teaser.png"/></div><div id="teaser-caption"><span class="keyword">Fig. 1:</span> Given an input pattern design we encode the geometry as a dual hypergraph, where nodes represent faces and hyperedges represent seams connecting two or more faces. We visualize the hyperedges with colored boundaries (left). In this work we prove that if this hypergraph is acyclic, the pattern design is foundation paper pieceable, and we present a leaf-plucking algorithm that iteratively removes leaf hyperedges, where a node is only contained in that hyperedge, to generate a sewing order for the design, which is the reverse of the order in which we plucked the nodes (center). Our quilt design tool shows the resulting sewing order by numbering the faces (center, Sewing order) and lets users color the faces to visualize the design. Quilters can use foundation paper piecing to sew the quilt by attaching fabric pieces one at a time in the sewing order and precisely construct the quilt top (right).<span></span></div><hr/><div class="links"><span class="keyword">Videos:</span><ul><li><a class="url">SIGGRAPH'21 long talk</a> (YouTube, 15 mins) </li><li><a class="url">SIGGRAPH'21 short talk</a> (YouTube, 5 mins) </li><li><a class="url">SIGGRAPH'21 fast forward</a> (YouTube, 30 sec) </li><li><a class="url">Paper overview</a> (YouTube, 5 mins)</li></ul></div><hr/><div class="links"><span class="keyword">Paper &amp; Supplemental materials:</span><ul><li><a class="url">Paper PDF</a> (PDF, 3 MB)</li><li><a class="url">Supplemental pattern images (50 designs and hypergraphs) </a> (PDF, 7 MB)</li><li><a class="url">Try our tool! </a> (in browser)</li><li><a class="url">Code </a> (Github)</li></ul></div><hr/><div class="links"><span class="keyword">News articles:</span><ul><li><a class="url">Stanford News</a></li><li><a class="url">Stanford Daily </a></li><li><a class="url">The Quilt Show Blog </a></li></ul></div><hr/><div class="links"><ul><li> To read about our latest work on foundation paper piecing, please see the <a class="url">webpage</a> for our UIST'22 paper: "Sketch-Based Design of Foundation Paper Pieceable Quilts."</li><li><span class="keyword">Questions? </span> Please reach out to <a>fppresearch2021@gmail.com</a>.</li></ul></div></div><footer></footer><style>body {
    font-family: Helvetica, Arial, sans-serif;
    font-weight: 300
    }
#container {
    margin: 0 auto;
    width: 70%;
    color: #2a2a2a
    }
#title h1, #authors {
    text-align: center;
    font-weight: 300
    }
#authors {
    width: 100%;
    margin: 5px auto
    }
.keyword {
    font-weight: 500;
    color: #000
    }
.url {
    font-weight: 500;
    color: #06f
    }
#authors ul {
    list-style-type: none;
    margin: 0 auto;
    padding: 0;
    overflow: hidden;
    font-size: 14pt
    }
#authors li {
    display: inline-block;
    margin: 0 20px
    }
#teaser img {
    width: 100%;
    margin-bottom: 10px
    }
#abstract {
    margin: 10px 0
    }
#abstract .keyword, #links .keyword {
    font-size: 14pt
    }
a {
    text-decoration: none
    }
.links ul {
    list-style-type: none;
    padding-left: 0
    }
.links li {
    margin-bottom: 20px
    }
.row {
    height: 15%;
    margin: 0 auto;
    text-align: center
    }
#top-caption {
    text-align: center
    }
footer {
    text-align: center;
    padding: 10px
    }</style></body></html>