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Graph."],"published-print":{"date-parts":[[2014,3]]},"abstract":"<jats:p>\n            This article introduces a method for accurately computing the visible contours of a smooth 3D surface for stylization. This is a surprisingly difficult problem, and previous methods are prone to topological errors, such as gaps in the outline. Our approach is to generate, for each viewpoint, a new triangle mesh with contours that are topologically equivalent and geometrically close to those of the original smooth surface. The contours of the mesh can then be rendered with exact visibility. The core of the approach is\n            <jats:italic>Contour Consistency,<\/jats:italic>\n            a way to prove topological equivalence between the contours of two surfaces. Producing a surface tessellation that satisfies this property is itself challenging; to this end, we introduce a type of triangle that ensures consistency at the contour. We then introduce an iterative mesh generation procedure, based on these ideas. This procedure does not fully guarantee consistency, but errors are not noticeable in our experiments. Our algorithm can operate on any smooth input surface representation; we use Catmull-Clark subdivision surfaces in our implementation. We demonstrate results computing contours of complex 3D objects, on which our method eliminates the contour artifacts of other methods.\n          <\/jats:p>","DOI":"10.1145\/2558307","type":"journal-article","created":{"date-parts":[[2014,4,15]],"date-time":"2014-04-15T17:50:29Z","timestamp":1397584229000},"page":"1-21","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":21,"title":["Computing smooth surface contours with accurate topology"],"prefix":"10.1145","volume":"33","author":[{"given":"Pierre","family":"B\u00e9nard","sequence":"first","affiliation":[{"name":"University of Toronto, Universit\u00e9 de Bordeaux, LaBRI, CNRS, and Inria, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Aaron","family":"Hertzmann","sequence":"additional","affiliation":[{"name":"Adobe Research, CA, University of Toronto, Canada and Pixar Animation Studios, CA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Michael","family":"Kass","sequence":"additional","affiliation":[{"name":"Pixar Animation Studios, CA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2014,4,8]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/800196.806007"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142994265292"},{"key":"e_1_2_2_3_1","volume-title":"Proceedings of the Symposium on Non-Photorealistic Animation and Rendering (NPAR'12)","author":"B\u00e9nard P.","unstructured":"P. B\u00e9nard , J. Lu , F. Cole , A. Finkelstein , and J. Thollot . 2012. Active strokes: Coherent line stylization for animated 3d models . In Proceedings of the Symposium on Non-Photorealistic Animation and Rendering (NPAR'12) . 37--46. P. B\u00e9nard, J. Lu, F. Cole, A. Finkelstein, and J. Thollot. 2012. Active strokes: Coherent line stylization for animated 3d models. In Proceedings of the Symposium on Non-Photorealistic Animation and Rendering (NPAR'12). 37--46."},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1145\/988437.988439"},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/2024676.2024690"},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/0010-4485(78)90110-0"},{"key":"e_1_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2009.102"},{"key":"e_1_2_2_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/882262.882354"},{"key":"e_1_2_2_9_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2008.01258.x"},{"key":"e_1_2_2_10_1","doi-asserted-by":"publisher","DOI":"10.1145\/97880.97890"},{"key":"e_1_2_2_11_1","volume-title":"Interactive non-photorealistic technical illustration. M. S. thesis","author":"Gooch A.","unstructured":"A. Gooch . 1998. Interactive non-photorealistic technical illustration. M. S. thesis , University of Utah. A. Gooch. 1998. Interactive non-photorealistic technical illustration. M. S. thesis, University of Utah."},{"key":"e_1_2_2_12_1","doi-asserted-by":"publisher","DOI":"10.1145\/1731047.1731056"},{"key":"e_1_2_2_13_1","doi-asserted-by":"publisher","DOI":"10.1080\/10867651.2003.10487592"},{"key":"e_1_2_2_14_1","doi-asserted-by":"publisher","DOI":"10.1145\/166117.166121"},{"key":"e_1_2_2_15_1","unstructured":"A. Hertzmann. 1999. Introduction to 3d non-photorealistic rendering: Silhouettes and outlines. In SIGGRAPH Course Notes on Non-Photorealistic Rendering S. Green Ed.  A. Hertzmann. 1999. Introduction to 3d non-photorealistic rendering: Silhouettes and outlines. In SIGGRAPH Course Notes on Non-Photorealistic Rendering S. Green Ed."},{"key":"e_1_2_2_16_1","doi-asserted-by":"publisher","DOI":"10.1145\/344779.345074"},{"key":"e_1_2_2_17_1","doi-asserted-by":"publisher","DOI":"10.1111\/1467-8659.00584"},{"key":"e_1_2_2_18_1","doi-asserted-by":"publisher","DOI":"10.1145\/882262.882355"},{"key":"e_1_2_2_19_1","doi-asserted-by":"publisher","DOI":"10.1145\/2024676.2024683"},{"key":"e_1_2_2_20_1","volume-title":"Proceedings of the Eurographics\/ACM SIGGRAPH Symposium on Geometry Processing (SGP'03)","author":"Kirsanov D.","unstructured":"D. Kirsanov , P. Sander , and S. Gortler . 2003. Simple silhouettes for complex surfaces . In Proceedings of the Eurographics\/ACM SIGGRAPH Symposium on Geometry Processing (SGP'03) . 102--106. D. Kirsanov, P. Sander, and S. Gortler. 2003. Simple silhouettes for complex surfaces. In Proceedings of the Eurographics\/ACM SIGGRAPH Symposium on Geometry Processing (SGP'03). 102--106."},{"key":"e_1_2_2_21_1","volume-title":"What does the occluding contour tell us about solid shape&quest","author":"Koenderink J. J.","unstructured":"J. J. Koenderink . 1984. What does the occluding contour tell us about solid shape&quest ; Percept . 13, 3, 321--330. J. J. Koenderink. 1984. What does the occluding contour tell us about solid shape&quest; Percept. 13, 3, 321--330."},{"key":"e_1_2_2_22_1","doi-asserted-by":"publisher","DOI":"10.1145\/258734.258894"},{"key":"e_1_2_2_23_1","doi-asserted-by":"publisher","DOI":"10.1145\/340916.340920"},{"key":"e_1_2_2_24_1","doi-asserted-by":"publisher","DOI":"10.1145\/1183287.1183288"},{"key":"e_1_2_2_25_1","doi-asserted-by":"publisher","DOI":"10.1145\/1183287.1183297"},{"key":"e_1_2_2_26_1","doi-asserted-by":"publisher","DOI":"10.1145\/97879.97901"},{"key":"e_1_2_2_27_1","doi-asserted-by":"publisher","DOI":"10.1145\/280814.280945"},{"key":"e_1_2_2_28_1","doi-asserted-by":"publisher","DOI":"10.1145\/237170.237287"}],"container-title":["ACM Transactions on Graphics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2558307","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/2558307","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T07:35:00Z","timestamp":1750232100000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2558307"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,3]]},"references-count":28,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2014,3]]}},"alternative-id":["10.1145\/2558307"],"URL":"https:\/\/doi.org\/10.1145\/2558307","relation":{},"ISSN":["0730-0301","1557-7368"],"issn-type":[{"value":"0730-0301","type":"print"},{"value":"1557-7368","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,3]]},"assertion":[{"value":"2013-04-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2013-12-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2014-04-08","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}