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Graph."],"published-print":{"date-parts":[[2014,7,27]]},"abstract":"<jats:p>Basic topological modeling, such as the ability to have several faces share a common edge, has been largely absent from vector graphics. We introduce the vector graphics complex (VGC) as a simple data structure to support fundamental topological modeling operations for vector graphics illustrations. The VGC can represent any arbitrary non-manifold topology as an immersion in the plane, unlike planar maps which can only represent embeddings. This allows for the direct representation of incidence relationships between objects and can therefore more faithfully capture the intended semantics of many illustrations, while at the same time keeping the geometric flexibility of stacking-based systems. We describe and implement a set of topological editing operations for the VGC, including glue, unglue, cut, and uncut. Our system maintains a global stacking order for all faces, edges, and vertices without requiring that components of an object reside together on a single layer. This allows for the coordinated editing of shared vertices and edges even for objects that have components distributed across multiple layers. We introduce VGC-specific methods that are tailored towards quickly achieving desired stacking orders for faces, edges, and vertices.<\/jats:p>","DOI":"10.1145\/2601097.2601169","type":"journal-article","created":{"date-parts":[[2014,7,22]],"date-time":"2014-07-22T15:08:20Z","timestamp":1406041700000},"page":"1-12","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":24,"title":["Vector graphics complexes"],"prefix":"10.1145","volume":"33","author":[{"given":"Boris","family":"Dalstein","sequence":"first","affiliation":[{"name":"University of British Columbia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"R\u00e9mi","family":"Ronfard","sequence":"additional","affiliation":[{"name":"University of Grenoble &amp; Inria, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michiel","family":"van de Panne","sequence":"additional","affiliation":[{"name":"University of British Columbia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2014,7,27]]},"reference":[{"key":"e_1_2_2_1_1","volume-title":"Adobe Illustrator: Help and tutorials.","author":"Adobe Systems Inc.","year":"2013","unstructured":"Adobe Systems Inc. , 2013 . 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Applied mathematics","author":"Edelsbrunner H.","year":"2010","unstructured":"Edelsbrunner , H. , and Harer , J . 2010 . Computational Topology: An Introduction. Applied mathematics . American Mathematical Society . Edelsbrunner, H., and Harer, J. 2010. Computational Topology: An Introduction. Applied mathematics. American Mathematical Society."},{"key":"e_1_2_2_9_1","doi-asserted-by":"publisher","DOI":"10.1145\/1531326.1531389"},{"key":"e_1_2_2_10_1","doi-asserted-by":"crossref","unstructured":"Granados M. Hachenberger P. Hert S. Kettner L. Mehlhorn K. and \n      Seel M\n  . \n  2003\n  . Boolean operations on 3D selective Nef complexes: Data structure algorithms and implementation. In Algorithms - ESA 2003 vol. \n  2832\n   of \n  Lecture Notes in Computer Science\n  . \n  Springer Berlin Heidelberg 654--666.  Granados M. Hachenberger P. Hert S. Kettner L. Mehlhorn K. and Seel M. 2003. Boolean operations on 3D selective Nef complexes: Data structure algorithms and implementation. 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Proceedings of the Third International Conference in Central Europe on Computer Graphics and Visualisation '95 1 (Feb.), 173--186 . Marcheix, D., and Gueorguieva, S. 1995. Topological operators for non-manifold modeling. Proceedings of the Third International Conference in Central Europe on Computer Graphics and Visualisation '95 1 (Feb.), 173--186."},{"key":"e_1_2_2_22_1","doi-asserted-by":"publisher","DOI":"10.1145\/1531326.1531390"},{"key":"e_1_2_2_23_1","unstructured":"Nef W. 1978. Beitr\u00e4ge zur Theorie der Polyeder: mit Anwendungen in der Computergraphik. Beitr\u00e4ge zur Mathematik Informatik und Nachrichtentechnik. Lang.  Nef W. 1978. Beitr\u00e4ge zur Theorie der Polyeder: mit Anwendungen in der Computergraphik . Beitr\u00e4ge zur Mathematik Informatik und Nachrichtentechnik. 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Watson Research Center, 145--180."},{"key":"e_1_2_2_28_1","doi-asserted-by":"publisher","DOI":"10.1145\/267734.267742"},{"key":"e_1_2_2_29_1","unstructured":"Shreiner D. Woo M. Neider J. and Davis T. 2004. Tesselators and quadrics. In The OpenGL Programming Guide Fourth Edition. Addison-Wesley ch. 11 487--514.  Shreiner D. Woo M. Neider J. and Davis T. 2004. Tesselators and quadrics. In The OpenGL Programming Guide Fourth Edition . Addison-Wesley ch. 11 487--514."},{"key":"e_1_2_2_30_1","doi-asserted-by":"publisher","DOI":"10.1145\/604471.604503"},{"key":"e_1_2_2_31_1","volume-title":"Scalable Vector Graphics (SVG) 1.1","author":"SVG Working Group","unstructured":"SVG Working Group , 2011. Scalable Vector Graphics (SVG) 1.1 ( Second Edition). http:\/\/www.w3.org\/TR\/SVG11\/. SVG Working Group, 2011. 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