{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T02:53:54Z","timestamp":1774925634029,"version":"3.50.1"},"reference-count":146,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2015,5,26]],"date-time":"2015-05-26T00:00:00Z","timestamp":1432598400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004730","name":"University of Toronto","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100004730","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["MIVIS PTDC\/EIA-EIA\/104031\/2008, CEDAR PTDC\/EIA-EIA\/116070\/2009, TECTON-3D PTDC\/EEI-SII\/3154\/2012, UID\/CEC\/50021\/2013"],"award-info":[{"award-number":["MIVIS PTDC\/EIA-EIA\/104031\/2008, CEDAR PTDC\/EIA-EIA\/116070\/2009, TECTON-3D PTDC\/EEI-SII\/3154\/2012, UID\/CEC\/50021\/2013"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Comput. Surv."],"published-print":{"date-parts":[[2015,7,21]]},"abstract":"<jats:p>Implicit surfaces (IS) are commonly used in image creation, modeling environments, modeling objects, and scientific data visualization. In this article, we present a survey of different techniques for fast visualization of IS. The main classes of visualization algorithms are identified along with the advantages of each in the context of the different types of IS commonly used in computer graphics. We focus closely on polygonization methods, as they are the most suited to fast visualization. Classification and comparison of existing approaches are presented using criteria extracted from current research. This enables the identification of the best strategies according to the number of specific requirements, such as speed, accuracy, quality, or stylization.<\/jats:p>","DOI":"10.1145\/2732197","type":"journal-article","created":{"date-parts":[[2015,5,27]],"date-time":"2015-05-27T18:11:50Z","timestamp":1432750310000},"page":"1-39","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":62,"title":["A Survey on Implicit Surface Polygonization"],"prefix":"10.1145","volume":"47","author":[{"given":"B. R.","family":"de Ara\u00fajo","sequence":"first","affiliation":[{"name":"University of Toronto, Toronto, ON, Canada"}]},{"given":"Daniel S.","family":"Lopes","sequence":"additional","affiliation":[{"name":"INESC-ID Lisboa, Lisboa, Portugal"}]},{"given":"Pauline","family":"Jepp","sequence":"additional","affiliation":[{"name":"INESC-ID Lisboa, Lisboa, Portugal"}]},{"given":"Joaquim A.","family":"Jorge","sequence":"additional","affiliation":[{"name":"INESC-ID Lisboa, Lisboa, Portugal"}]},{"given":"Brian","family":"Wyvill","sequence":"additional","affiliation":[{"name":"University of Victoria, BC, Canada"}]}],"member":"320","published-online":{"date-parts":[[2015,5,26]]},"reference":[{"key":"e_1_2_1_1_1","volume-title":"The Computational Geometry Algorithms Library Home Page. Retrieved","author":"CGAL.","year":"2015","unstructured":"CGAL. 2014. The Computational Geometry Algorithms Library Home Page. Retrieved April 1, 2015 , from http:\/\/www.cgal.org. CGAL. 2014. The Computational Geometry Algorithms Library Home Page. Retrieved April 1, 2015, from http:\/\/www.cgal.org."},{"key":"e_1_2_1_2_1","volume-title":"ImplicitMesher Home Page. Retrieved","year":"2015","unstructured":"ImplicitMesher. 2014. ImplicitMesher Home Page. Retrieved April 1, 2015 , from http:\/\/www.dgp.toronto.edu\/&sim;rms\/software\/ImplicitMesher\/index.html. ImplicitMesher. 2014. ImplicitMesher Home Page. Retrieved April 1, 2015, from http:\/\/www.dgp.toronto.edu\/&sim;rms\/software\/ImplicitMesher\/index.html."},{"key":"e_1_2_1_3_1","volume-title":"VTK Home Page. Retrieved","author":"VTK.","year":"2015","unstructured":"VTK. 2014. VTK Home Page. Retrieved April 1, 2015 , from http:\/\/www.vtk.org\/. VTK. 2014. VTK Home Page. Retrieved April 1, 2015, from http:\/\/www.vtk.org\/."},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1111\/1467-8659.00479"},{"key":"e_1_2_1_5_1","volume-title":"Mathematical Methods for Curves and Surfaces: Tromso \u201904","author":"Alberti Lionel","unstructured":"Lionel Alberti , Georges Comte , and Bernard Mourrain . 2005. Meshing implicit algebraic surfaces: The smooth case . In Mathematical Methods for Curves and Surfaces: Tromso \u201904 , L. L. Schumaker, M. Maehlen, and K. Morken (Eds.). Nashboro , 11--26. Lionel Alberti, Georges Comte, and Bernard Mourrain. 2005. Meshing implicit algebraic surfaces: The smooth case. In Mathematical Methods for Curves and Surfaces: Tromso \u201904, L. L. Schumaker, M. Maehlen, and K. Morken (Eds.). Nashboro, 11--26."},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.gmod.2005.09.001"},{"key":"e_1_2_1_7_1","volume-title":"Proceedings of the 2003 Eurographics\/ACM SIGGRAPH Symposium on Geometry Processing (SGP\u201903)","author":"Attene Marco","year":"2003","unstructured":"Marco Attene , Bianca Falcidieno , Jarek Rossignac , and Michela Spagnuolo . 2003 . Edge-sharpener: Recovering sharp features in triangulations of non-adaptively re-meshed surfaces . In Proceedings of the 2003 Eurographics\/ACM SIGGRAPH Symposium on Geometry Processing (SGP\u201903) . 62--69. Marco Attene, Bianca Falcidieno, Jarek Rossignac, and Michela Spagnuolo. 2003. Edge-sharpener: Recovering sharp features in triangulations of non-adaptively re-meshed surfaces. In Proceedings of the 2003 Eurographics\/ACM SIGGRAPH Symposium on Geometry Processing (SGP\u201903). 62--69."},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1109\/SMI.2005.5"},{"key":"e_1_2_1_9_1","volume-title":"Schikore","author":"Bajaj Chandrajit L.","year":"1999","unstructured":"Chandrajit L. Bajaj , Valerio Pascucci , and Daniel R . Schikore . 1999 . Accelerated isocontouring of scalar fields. In Data Visualization Techniques. Trends in Software, Vol. 6 . John Wiley and Sons , 31--47. Chandrajit L. Bajaj, Valerio Pascucci, and Daniel R. Schikore. 1999. Accelerated isocontouring of scalar fields. In Data Visualization Techniques. Trends in Software, Vol. 6. John Wiley and Sons, 31--47."},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1142\/S021865430200008X"},{"key":"e_1_2_1_11_1","volume-title":"Proceedings of the Computer Graphics International Conference (CGI\u201998)","author":"Belyaev Alexander G.","year":"1998","unstructured":"Alexander G. Belyaev , Alexander A. Pasko , and Tosiyasu L. Kunii . 1998. Ridges and ravines on implicit surfaces . In Proceedings of the Computer Graphics International Conference (CGI\u201998) . 530. DOI:http:\/\/dx.doi.org\/10.1109\/CGI. 1998 .694306 10.1109\/CGI.1998.694306 Alexander G. Belyaev, Alexander A. Pasko, and Tosiyasu L. Kunii. 1998. Ridges and ravines on implicit surfaces. In Proceedings of the Computer Graphics International Conference (CGI\u201998). 530. DOI:http:\/\/dx.doi.org\/10.1109\/CGI.1998.694306"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1007\/11537908_4"},{"key":"e_1_2_1_13_1","volume-title":"Silva","author":"Berger Matthew","year":"2014","unstructured":"Matthew Berger , Andrea Tagliasacchi , Lee M. Seversky , Pierre Alliez , Joshua A. Levine , Andrei Sharf , and Claudio T . Silva . 2014 . State of the art in surface reconstruction from point clouds. In Eurographics 2014\u2014State of the Art Reports, S. Lefebvre and M. Spagnuolo (Eds.). Eurographics Association . DOI:http:\/\/dx.doi.org\/10.2312\/egst.20141040 10.2312\/egst.20141040 Matthew Berger, Andrea Tagliasacchi, Lee M. Seversky, Pierre Alliez, Joshua A. Levine, Andrei Sharf, and Claudio T. Silva. 2014. State of the art in surface reconstruction from point clouds. In Eurographics 2014\u2014State of the Art Reports, S. Lefebvre and M. Spagnuolo (Eds.). Eurographics Association. DOI:http:\/\/dx.doi.org\/10.2312\/egst.20141040"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1145\/357306.357310"},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1016\/0167-8396(88)90013-1"},{"key":"e_1_2_1_16_1","volume-title":"An implicit surface polygonizer","author":"Bloomenthal Jules","unstructured":"Jules Bloomenthal . 1994. An implicit surface polygonizer . In Graphics Gems IV, Paul Heckbert (Ed.). Academic Press , Boston, MA , 324--349. Jules Bloomenthal. 1994. An implicit surface polygonizer. In Graphics Gems IV, Paul Heckbert (Ed.). Academic Press, Boston, MA, 324--349."},{"key":"e_1_2_1_18_1","volume-title":"Introduction to Implicit Surfaces. Morgan Kaufmann","author":"Bloomenthal Jules","unstructured":"Jules Bloomenthal and Chandrajit Bajaj . 1997. Introduction to Implicit Surfaces. Morgan Kaufmann , San Francisco, CA . Jules Bloomenthal and Chandrajit Bajaj. 1997. Introduction to Implicit Surfaces. Morgan Kaufmann, San Francisco, CA."},{"key":"e_1_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1145\/218380.218462"},{"key":"e_1_2_1_20_1","volume-title":"Proceedings of GraphiCon","author":"Bogaevski Ilia","year":"2003","unstructured":"Ilia Bogaevski , Veronique Lang , Alexander Belyaev , and Tosiyasu L. Kunii . 2003. Color ridges on implicit polynomial surfaces . In Proceedings of GraphiCon 2003 . 161--164. Ilia Bogaevski, Veronique Lang, Alexander Belyaev, and Tosiyasu L. Kunii. 2003. Color ridges on implicit polynomial surfaces. In Proceedings of GraphiCon 2003. 161--164."},{"key":"e_1_2_1_21_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.gmod.2005.01.004"},{"key":"e_1_2_1_22_1","volume-title":"Proceedings of Implicit Surfaces \u201996","author":"Bottino Andrea","year":"1996","unstructured":"Andrea Bottino , Wim Nuij , and Kees Van Overveld . 1996 . How to shrinkwrap through a critical point: An algorithm for the adaptive triangulation of iso-surfaces with arbitrary topology . In Proceedings of Implicit Surfaces \u201996 . 53--72. Andrea Bottino, Wim Nuij, and Kees Van Overveld. 1996. How to shrinkwrap through a critical point: An algorithm for the adaptive triangulation of iso-surfaces with arbitrary topology. In Proceedings of Implicit Surfaces \u201996. 53--72."},{"key":"e_1_2_1_23_1","doi-asserted-by":"publisher","DOI":"10.1145\/1268517.1268521"},{"key":"e_1_2_1_24_1","volume-title":"Proceedings of Implicit Surfaces \u201998","author":"David","unstructured":"David J. Bremer and John F. Hughes. 1998. Rapid approximate silhouette rendering of implicit surfaces . In Proceedings of Implicit Surfaces \u201998 . 155--164. David J. Bremer and John F. Hughes. 1998. Rapid approximate silhouette rendering of implicit surfaces. In Proceedings of Implicit Surfaces \u201998. 155--164."},{"key":"e_1_2_1_25_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2011.02058.x"},{"key":"e_1_2_1_26_1","doi-asserted-by":"publisher","DOI":"10.1145\/383259.383266"},{"key":"e_1_2_1_27_1","volume-title":"Proceedings of the 16th Conference on Scientific Computing (Algoritmy\u201902)","author":"Cerm\u00e1k Martin","year":"2002","unstructured":"Martin Cerm\u00e1k and V\u00e1clav Skala . 2002 . Polygonization by the edge spinning . In Proceedings of the 16th Conference on Scientific Computing (Algoritmy\u201902) . Martin Cerm\u00e1k and V\u00e1clav Skala. 2002. Polygonization by the edge spinning. In Proceedings of the 16th Conference on Scientific Computing (Algoritmy\u201902)."},{"key":"e_1_2_1_28_1","doi-asserted-by":"publisher","DOI":"10.5555\/1009379.1009574"},{"key":"e_1_2_1_29_1","doi-asserted-by":"publisher","DOI":"10.1504\/IJCSE.2007.014464"},{"key":"e_1_2_1_30_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0097-8493(97)00085-X"},{"key":"e_1_2_1_31_1","doi-asserted-by":"publisher","DOI":"10.1145\/997817.997861"},{"key":"e_1_2_1_33_1","doi-asserted-by":"publisher","DOI":"10.1145\/160985.161150"},{"key":"e_1_2_1_34_1","doi-asserted-by":"publisher","DOI":"10.5555\/584110.584123"},{"key":"e_1_2_1_35_1","doi-asserted-by":"publisher","DOI":"10.5555\/1025131.1026261"},{"key":"e_1_2_1_36_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cag.2005.08.027"},{"key":"e_1_2_1_37_1","doi-asserted-by":"publisher","DOI":"10.1109\/SIBGRAPI.2005.2"},{"key":"e_1_2_1_38_1","doi-asserted-by":"publisher","DOI":"10.5555\/155294.155323"},{"key":"e_1_2_1_39_1","volume-title":"Proceedings of Implicit Surfaces \u201995","author":"Desbrun Mathieu","year":"1995","unstructured":"Mathieu Desbrun , Nicolas Tsingos , and Marie-Paule Gascuel . 1995 . Adaptive sampling of implicit surfaces for interactive modeling and animation . In Proceedings of Implicit Surfaces \u201995 . Mathieu Desbrun, Nicolas Tsingos, and Marie-Paule Gascuel. 1995. Adaptive sampling of implicit surfaces for interactive modeling and animation. In Proceedings of Implicit Surfaces \u201995."},{"key":"e_1_2_1_40_1","doi-asserted-by":"publisher","DOI":"10.1109\/SMI.2007.15"},{"key":"e_1_2_1_41_1","doi-asserted-by":"publisher","DOI":"10.1109\/MCSE.2009.34"},{"key":"e_1_2_1_42_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2008.60"},{"key":"e_1_2_1_43_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2005.00851.x"},{"key":"e_1_2_1_44_1","volume-title":"Meshing Implicit Curves and Surfaces","author":"Frey Pascal Jean","unstructured":"Pascal Jean Frey and Paul-Louis George . 2010. Meshing Implicit Curves and Surfaces . ISTE , London, UK . DOI:http:\/\/dx.doi.org\/10.1002\/9780470611166.ch16 10.1002\/9780470611166.ch16 Pascal Jean Frey and Paul-Louis George. 2010. Meshing Implicit Curves and Surfaces. ISTE, London, UK. DOI:http:\/\/dx.doi.org\/10.1002\/9780470611166.ch16"},{"key":"e_1_2_1_45_1","doi-asserted-by":"publisher","DOI":"10.1006\/gmod.1999.0514"},{"key":"e_1_2_1_46_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cag.2009.03.016"},{"key":"e_1_2_1_47_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00371-008-0297-x"},{"key":"e_1_2_1_48_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cagd.2005.06.005"},{"key":"e_1_2_1_49_1","volume-title":"Implicit Curves and Surfaces: Mathematics, Data Structures and Algorithms","author":"Gomes Abel","unstructured":"Abel Gomes , Irina Voiculescu , Joaquim Jorge , Brian Wyvill , and Callum Galbraith . 2009. Implicit Curves and Surfaces: Mathematics, Data Structures and Algorithms . Springer . Abel Gomes, Irina Voiculescu, Joaquim Jorge, Brian Wyvill, and Callum Galbraith. 2009. Implicit Curves and Surfaces: Mathematics, Data Structures and Algorithms. Springer."},{"key":"e_1_2_1_50_1","doi-asserted-by":"publisher","DOI":"10.1109\/CEC.2010.5586012"},{"key":"e_1_2_1_51_1","volume-title":"Modern Differential Geometry of Curves and Surfaces with Mathematica","author":"Gray Alfred","unstructured":"Alfred Gray . 1996. Modern Differential Geometry of Curves and Surfaces with Mathematica . CRC Press , Boca Raton, FL . Alfred Gray. 1996. Modern Differential Geometry of Curves and Surfaces with Mathematica. CRC Press, Boca Raton, FL."},{"key":"e_1_2_1_52_1","unstructured":"Markus Hadwiger Joe M. Kniss Christof Rezk-salama Daniel Weiskopf and Klaus Engel. 2006. Real-Time Volume Graphics. A. K. Peters Ltd. Natick MA.   Markus Hadwiger Joe M. Kniss Christof Rezk-salama Daniel Weiskopf and Klaus Engel. 2006. Real-Time Volume Graphics. A. K. Peters Ltd. Natick MA."},{"key":"e_1_2_1_53_1","doi-asserted-by":"publisher","DOI":"10.1109\/38.62694"},{"key":"e_1_2_1_54_1","volume-title":"Proceedings of the 3rd Conference on Visualization \u201992 (VIS\u201992)","author":"Charles","year":"1992","unstructured":"Charles D. Hansen and Paul Hinker. 1992. Massively parallel isosurface extraction . In Proceedings of the 3rd Conference on Visualization \u201992 (VIS\u201992) . 77--83. DOI:http:\/\/dx.doi.org\/10.1109\/VISUAL. 1992 .235223 10.1109\/VISUAL.1992.235223 Charles D. Hansen and Paul Hinker. 1992. Massively parallel isosurface extraction. In Proceedings of the 3rd Conference on Visualization \u201992 (VIS\u201992). 77--83. DOI:http:\/\/dx.doi.org\/10.1109\/VISUAL.1992.235223"},{"key":"e_1_2_1_55_1","volume-title":"Mathematical Visualization","author":"Hart John C.","unstructured":"John C. Hart . 1997. Morse theory for implicit surface modeling . In Mathematical Visualization . Springer-Verlag , 257--268. John C. Hart. 1997. Morse theory for implicit surface modeling. In Mathematical Visualization. Springer-Verlag, 257--268."},{"key":"e_1_2_1_56_1","doi-asserted-by":"publisher","DOI":"10.1007\/s003710050126"},{"key":"e_1_2_1_57_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0925-7721(99)00030-9"},{"key":"e_1_2_1_59_1","volume-title":"Marching Triangles: Delaunay Implicit Surface Triangulation. Technical Report 01","author":"Hilton Adrian","year":"1997","unstructured":"Adrian Hilton and John Illingworth . 1997 . Marching Triangles: Delaunay Implicit Surface Triangulation. Technical Report 01 . University of Surrey , Guidford , CVSSP. Adrian Hilton and John Illingworth. 1997. Marching Triangles: Delaunay Implicit Surface Triangulation. Technical Report 01. University of Surrey, Guidford, CVSSP."},{"key":"e_1_2_1_60_1","doi-asserted-by":"publisher","DOI":"10.1109\/ICIP.1996.560840"},{"key":"e_1_2_1_61_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2005.00879.x"},{"key":"e_1_2_1_62_1","doi-asserted-by":"publisher","DOI":"10.1111\/1467-8659.00302"},{"key":"e_1_2_1_64_1","doi-asserted-by":"publisher","DOI":"10.1109\/SIBGRAPI.2008.18"},{"key":"e_1_2_1_65_1","doi-asserted-by":"publisher","DOI":"10.1145\/1188966.1189018"},{"key":"e_1_2_1_66_1","doi-asserted-by":"publisher","DOI":"10.1145\/1188966.1189018"},{"key":"e_1_2_1_67_1","doi-asserted-by":"publisher","DOI":"10.1145\/566570.566586"},{"key":"e_1_2_1_68_1","doi-asserted-by":"publisher","DOI":"10.1145\/74333.74364"},{"key":"e_1_2_1_69_1","doi-asserted-by":"publisher","DOI":"10.1145\/1174429.1174455"},{"key":"e_1_2_1_70_1","doi-asserted-by":"publisher","DOI":"10.1109\/38.909016"},{"key":"e_1_2_1_71_1","volume-title":"Proceedings of the 5th Eurographics Symposium on Geometry Processing (SGP\u201907)","author":"Kazhdan Michael","year":"2007","unstructured":"Michael Kazhdan , Allison Klein , Ketan Dalal , and Hugues Hoppe . 2007 . Unconstrained isosurface extraction on arbitrary octrees . In Proceedings of the 5th Eurographics Symposium on Geometry Processing (SGP\u201907) . 125--133. http:\/\/dl.acm.org\/citation.cfm&quest;id&equals;1281991.1282009 Michael Kazhdan, Allison Klein, Ketan Dalal, and Hugues Hoppe. 2007. Unconstrained isosurface extraction on arbitrary octrees. In Proceedings of the 5th Eurographics Symposium on Geometry Processing (SGP\u201907). 125--133. http:\/\/dl.acm.org\/citation.cfm&quest;id&equals;1281991.1282009"},{"key":"e_1_2_1_72_1","first-page":"241","article-title":"GPU construction and transparent rendering of iso-surfaces","volume":"2005","author":"Kipfer Peter","year":"2005","unstructured":"Peter Kipfer and R\u00fcdiger Westermann . 2005 . GPU construction and transparent rendering of iso-surfaces . In Proceedings of Vision, Modeling, and Visualization 2005. 241 -- 248 . Peter Kipfer and R\u00fcdiger Westermann. 2005. GPU construction and transparent rendering of iso-surfaces. In Proceedings of Vision, Modeling, and Visualization 2005. 241--248.","journal-title":"Proceedings of Vision, Modeling, and Visualization"},{"key":"e_1_2_1_74_1","volume-title":"Proceedings of the IEEE Symposium on Interactive Ray Tracing. 115--124","author":"Knoll Aaron","unstructured":"Aaron Knoll , Ingo Wald , Steven G. Parker , and Charles D. Hansen . 2006. Interactive isosurface ray tracing of large octree volumes . In Proceedings of the IEEE Symposium on Interactive Ray Tracing. 115--124 . Aaron Knoll, Ingo Wald, Steven G. Parker, and Charles D. Hansen. 2006. Interactive isosurface ray tracing of large octree volumes. In Proceedings of the IEEE Symposium on Interactive Ray Tracing. 115--124."},{"key":"e_1_2_1_75_1","doi-asserted-by":"publisher","DOI":"10.1145\/984952.984956"},{"key":"e_1_2_1_76_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cag.2004.08.009"},{"key":"e_1_2_1_77_1","doi-asserted-by":"publisher","DOI":"10.1145\/383259.383265"},{"key":"e_1_2_1_78_1","volume-title":"Solid Shape","author":"Koenderink Jan J.","unstructured":"Jan J. Koenderink . 1990. Solid Shape . MIT Press , Cambridge, MA . Jan J. Koenderink. 1990. Solid Shape. MIT Press, Cambridge, MA."},{"key":"e_1_2_1_79_1","volume-title":"Proceedings of the Winter School of Computer Graphics Conference (WSCG\u201905)","author":"Levet Florian","year":"2005","unstructured":"Florian Levet , Julien Hadim , Patrick Reuter , and Christophe Schlick . 2005 . Anisotropic sampling for differential point rendering of implicit surfaces . In Proceedings of the Winter School of Computer Graphics Conference (WSCG\u201905) . 109--116. Florian Levet, Julien Hadim, Patrick Reuter, and Christophe Schlick. 2005. Anisotropic sampling for differential point rendering of implicit surfaces. In Proceedings of the Winter School of Computer Graphics Conference (WSCG\u201905). 109--116."},{"key":"e_1_2_1_80_1","doi-asserted-by":"publisher","DOI":"10.1080\/10867651.2003.10487582"},{"key":"e_1_2_1_81_1","doi-asserted-by":"publisher","DOI":"10.1109\/CAD-CG.2005.46"},{"key":"e_1_2_1_82_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2003.1175094"},{"key":"e_1_2_1_83_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cad.2012.11.003"},{"key":"e_1_2_1_84_1","doi-asserted-by":"publisher","DOI":"10.1145\/37401.37422"},{"key":"e_1_2_1_85_1","doi-asserted-by":"publisher","DOI":"10.5555\/951087.951140"},{"key":"e_1_2_1_87_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2007.70604"},{"key":"e_1_2_1_88_1","doi-asserted-by":"publisher","DOI":"10.5555\/951087.951139"},{"key":"e_1_2_1_89_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01900830"},{"key":"e_1_2_1_90_1","volume-title":"Mesh Displacement: An Improved Contouring Method for Trivariate Data. Technical Report.","author":"Moore Doug","year":"1995","unstructured":"Doug Moore and Joe Warren . 1995 . Mesh Displacement: An Improved Contouring Method for Trivariate Data. Technical Report. Doug Moore and Joe Warren. 1995. Mesh Displacement: An Improved Contouring Method for Trivariate Data. Technical Report."},{"key":"e_1_2_1_91_1","doi-asserted-by":"publisher","DOI":"10.5555\/882486.884073"},{"key":"e_1_2_1_92_1","doi-asserted-by":"publisher","DOI":"10.1145\/122718.122743"},{"key":"e_1_2_1_93_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01900699"},{"key":"e_1_2_1_94_1","volume-title":"Proceedings of the Conference on Visualization \u201997 (VIS\u201997)","author":"Neugebauer Peter","year":"1997","unstructured":"Peter Neugebauer and Konrad Klein . 1997 . Adaptive triangulation of objects reconstructed from multiple range images . In Proceedings of the Conference on Visualization \u201997 (VIS\u201997) . Peter Neugebauer and Konrad Klein. 1997. Adaptive triangulation of objects reconstructed from multiple range images. In Proceedings of the Conference on Visualization \u201997 (VIS\u201997)."},{"key":"e_1_2_1_95_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2003.1207437"},{"key":"e_1_2_1_96_1","doi-asserted-by":"publisher","DOI":"10.1109\/VISUAL.2004.28"},{"key":"e_1_2_1_97_1","volume-title":"Proceedings of the 2nd Conference on Visualization \u201991 (VIS\u201991)","author":"Gregory","unstructured":"Gregory M. Nielson and Bernd Hamann. 1991. The asymptotic decider: Resolving the ambiguity in marching cubes . In Proceedings of the 2nd Conference on Visualization \u201991 (VIS\u201991) . IEEE, Los Alamitos, CA, 83--91. http:\/\/dl.acm.org\/citation.cfm&quest;id&equals;949607.949621. Gregory M. Nielson and Bernd Hamann. 1991. The asymptotic decider: Resolving the ambiguity in marching cubes. In Proceedings of the 2nd Conference on Visualization \u201991 (VIS\u201991). IEEE, Los Alamitos, CA, 83--91. http:\/\/dl.acm.org\/citation.cfm&quest;id&equals;949607.949621."},{"key":"e_1_2_1_98_1","doi-asserted-by":"publisher","DOI":"10.1109\/38.252552"},{"key":"e_1_2_1_99_1","first-page":"718","article-title":"Object modelling by distribution function and a method of image generation","volume":"4","author":"Nishimura Hiromitsu","year":"1985","unstructured":"Hiromitsu Nishimura , Masashi Hirai , Tsuyoshi Kawai , Tory Kawata , Isao Shirakawa , and Kengo Omura . 1985 . Object modelling by distribution function and a method of image generation . Transactions of the IEICE Japan J68-D , 4 , 718 -- 725 . Hiromitsu Nishimura, Masashi Hirai, Tsuyoshi Kawai, Tory Kawata, Isao Shirakawa, and Kengo Omura. 1985. Object modelling by distribution function and a method of image generation. Transactions of the IEICE Japan J68-D, 4, 718--725.","journal-title":"Transactions of the IEICE Japan J68-D"},{"key":"e_1_2_1_100_1","doi-asserted-by":"publisher","DOI":"10.1145\/1201775.882293"},{"key":"e_1_2_1_101_1","doi-asserted-by":"publisher","DOI":"10.5555\/882486.884074"},{"key":"e_1_2_1_102_1","doi-asserted-by":"publisher","DOI":"10.1145\/1015706.1015768"},{"key":"e_1_2_1_103_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.gmod.2004.06.003"},{"key":"e_1_2_1_104_1","doi-asserted-by":"publisher","DOI":"10.1145\/566282.566308"},{"key":"e_1_2_1_105_1","volume-title":"Fedkiw","author":"Osher Stanley","year":"2003","unstructured":"Stanley Osher and Ronald P . Fedkiw . 2003 . Level Set Methods and Dynamic Implicit Surfaces. Springer , New York, NY. Stanley Osher and Ronald P. Fedkiw. 2003. Level Set Methods and Dynamic Implicit Surfaces. Springer, New York, NY."},{"key":"e_1_2_1_106_1","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(88)90002-2"},{"key":"e_1_2_1_107_1","doi-asserted-by":"publisher","DOI":"10.1109\/SIBGRAPI.2006.40"},{"key":"e_1_2_1_108_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02464333"},{"key":"e_1_2_1_109_1","doi-asserted-by":"publisher","DOI":"10.1016\/0097-8493(88)90070-2"},{"key":"e_1_2_1_110_1","doi-asserted-by":"publisher","DOI":"10.1002\/fld.1362"},{"key":"e_1_2_1_112_1","volume-title":"DistMesh\u2014A Simple Mesh Generator in MATLAB. Retrieved","author":"Persson Per-Olof","year":"2015","unstructured":"Per-Olof Persson . 2014. DistMesh\u2014A Simple Mesh Generator in MATLAB. Retrieved April 1, 2015 , from http:\/\/persson.berkeley.edu\/distmesh\/. Per-Olof Persson. 2014. DistMesh\u2014A Simple Mesh Generator in MATLAB. Retrieved April 1, 2015, from http:\/\/persson.berkeley.edu\/distmesh\/."},{"key":"e_1_2_1_113_1","doi-asserted-by":"publisher","DOI":"10.1145\/1057432.1057465"},{"key":"e_1_2_1_114_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00371-006-0083-6"},{"key":"e_1_2_1_115_1","volume-title":"Vetterling","author":"Press William H.","year":"1986","unstructured":"William H. Press , Brian P. Flannery , Saul A. Teukolsky , and William T . Vetterling . 1986 . Numerical Recipes\u2014The Art of Scientific Computing. Cambridge University Press , Cambridge, MA. William H. Press, Brian P. Flannery, Saul A. Teukolsky, and William T. Vetterling. 1986. Numerical Recipes\u2014The Art of Scientific Computing. Cambridge University Press, Cambridge, MA."},{"key":"e_1_2_1_116_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2008.01209.x"},{"key":"e_1_2_1_117_1","doi-asserted-by":"publisher","DOI":"10.1109\/CIT.2005.44"},{"key":"e_1_2_1_119_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.comgeo.2006.11.008"},{"key":"e_1_2_1_120_1","doi-asserted-by":"publisher","DOI":"10.1111\/1467-8659.00196"},{"key":"e_1_2_1_121_1","first-page":"765","article-title":"On the analytical description of some geometric objects","volume":"153","author":"Rvachev Vladimir L.","year":"1963","unstructured":"Vladimir L. Rvachev . 1963 . On the analytical description of some geometric objects . Reports of Ukrainian Academy of Sciences 153 , 4, 765 -- 767 . Vladimir L. Rvachev. 1963. On the analytical description of some geometric objects. Reports of Ukrainian Academy of Sciences 153, 4, 765--767.","journal-title":"Reports of Ukrainian Academy of Sciences"},{"key":"e_1_2_1_122_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2007.1012"},{"key":"e_1_2_1_123_1","doi-asserted-by":"publisher","DOI":"10.5555\/1025128.1026029"},{"key":"e_1_2_1_124_1","doi-asserted-by":"publisher","DOI":"10.1109\/SMI.2005.25"},{"key":"e_1_2_1_125_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2006.149"},{"key":"e_1_2_1_126_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2006.00972.x"},{"key":"e_1_2_1_127_1","doi-asserted-by":"publisher","DOI":"10.1017\/S096249290631001X"},{"key":"e_1_2_1_128_1","volume-title":"Eurographics Symposium on Parallel Graphics and Visualization, H. Childs, T. Kuhlen, and F. Marton (Eds.). Eurographics Association, 89--98","author":"Shirazian Pourya","year":"2012","unstructured":"Pourya Shirazian , Brian Wyvill , and Jean-Luc Duprat . 2012 . Polygonization of implicit surfaces on multi-core architectures with SIMD instructions . In Eurographics Symposium on Parallel Graphics and Visualization, H. Childs, T. Kuhlen, and F. Marton (Eds.). Eurographics Association, 89--98 . http:\/\/dblp.uni-trier.de\/db\/conf\/egpgv\/egpgv2012.html#ShirazianWD12. Pourya Shirazian, Brian Wyvill, and Jean-Luc Duprat. 2012. Polygonization of implicit surfaces on multi-core architectures with SIMD instructions. In Eurographics Symposium on Parallel Graphics and Visualization, H. Childs, T. Kuhlen, and F. Marton (Eds.). Eurographics Association, 89--98. http:\/\/dblp.uni-trier.de\/db\/conf\/egpgv\/egpgv2012.html#ShirazianWD12."},{"key":"e_1_2_1_130_1","first-page":"9","article-title":"A survey of GPU-based volume rendering of unstructured grids","volume":"12","author":"Silva Cl\u00e1udio T.","year":"2005","unstructured":"Cl\u00e1udio T. Silva , Joo L. D. Comba , Steven P. Callahan , and Fabio F. Bernardon . 2005 . A survey of GPU-based volume rendering of unstructured grids . Brazilian Journal of Theoretic and Applied Computing 12 , 9 -- 29 . Cl\u00e1udio T. Silva, Joo L. D. Comba, Steven P. Callahan, and Fabio F. Bernardon. 2005. A survey of GPU-based volume rendering of unstructured grids. Brazilian Journal of Theoretic and Applied Computing 12, 9--29.","journal-title":"Brazilian Journal of Theoretic and Applied Computing"},{"key":"e_1_2_1_131_1","volume-title":"Proceedings of the West Side Computer Graphics Conference (WSCG\u201998)","author":"Siqueira Marcelo F.","unstructured":"Marcelo F. Siqueira , S. R. Freitas , A. C. Filho , and G. Tavares . 1998. Speeding up adaptive polygonization . In Proceedings of the West Side Computer Graphics Conference (WSCG\u201998) . 11--12. Marcelo F. Siqueira, S. R. Freitas, A. C. Filho, and G. Tavares. 1998. Speeding up adaptive polygonization. In Proceedings of the West Side Computer Graphics Conference (WSCG\u201998). 11--12."},{"key":"e_1_2_1_132_1","volume-title":"Proceedings of the Western Computer Graphics Symposium.","author":"Barton","unstructured":"Barton T. Stander and John C. Hart. 1995. Interactive re-polygonization of blobby implicit curves . In Proceedings of the Western Computer Graphics Symposium. Barton T. Stander and John C. Hart. 1995. Interactive re-polygonization of blobby implicit curves. In Proceedings of the Western Computer Graphics Symposium."},{"key":"e_1_2_1_133_1","doi-asserted-by":"publisher","DOI":"10.1145\/258734.258868"},{"key":"e_1_2_1_134_1","doi-asserted-by":"publisher","DOI":"10.1109\/SMI.2005.2"},{"key":"e_1_2_1_135_1","series-title":"Lecture Notes in Computer Science","volume-title":"Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications","author":"Taubin Gabriel","unstructured":"Gabriel Taubin . 2012. Smooth signed distance surface reconstruction and applications . In Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications . Lecture Notes in Computer Science , Vol. 7441 . Springer , 38--45. DOI:http:\/\/dx.doi.org\/10.1007\/978-3-642-33275-3&lowbar;4 10.1007\/978-3-642-33275-3&lowbar;4 Gabriel Taubin. 2012. Smooth signed distance surface reconstruction and applications. In Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications. Lecture Notes in Computer Science, Vol. 7441. Springer, 38--45. DOI:http:\/\/dx.doi.org\/10.1007\/978-3-642-33275-3&lowbar;4"},{"key":"e_1_2_1_136_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.gmod.2005.09.003"},{"key":"e_1_2_1_137_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0097-8493(99)00076-X"},{"key":"e_1_2_1_138_1","doi-asserted-by":"publisher","DOI":"10.1145\/604471.604508"},{"key":"e_1_2_1_139_1","volume-title":"Proceedings of the 2001 WSCG International Conference (WSCG\u201901)","author":"Triquet Frederic","year":"2001","unstructured":"Frederic Triquet , Philippe Meseure , and Christophe Chaillou . 2001 . Fast polygonization of implicit surfaces . In Proceedings of the 2001 WSCG International Conference (WSCG\u201901) . 283--290. http:\/\/wscg.zcu.cz. Frederic Triquet, Philippe Meseure, and Christophe Chaillou. 2001. Fast polygonization of implicit surfaces. In Proceedings of the 2001 WSCG International Conference (WSCG\u201901). 283--290. http:\/\/wscg.zcu.cz."},{"key":"e_1_2_1_140_1","doi-asserted-by":"publisher","DOI":"10.1145\/311535.311580"},{"key":"e_1_2_1_141_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00371-002-0197-4"},{"key":"e_1_2_1_142_1","doi-asserted-by":"publisher","DOI":"10.1109\/VISUAL.2003.1250360"},{"key":"e_1_2_1_143_1","doi-asserted-by":"publisher","DOI":"10.1145\/1057432.1057464"},{"key":"e_1_2_1_144_1","first-page":"211","volume-title":"Proceedings of the Eurographics Symposium on Geometry Processing. 211--221","author":"Varadhan Gokul","year":"2006","unstructured":"Gokul Varadhan , Shankar Krishnan , Liangjun Zhang , and Dinesh Manocha . 2006 . Reliable implicit surface polygonization using visibility mapping . In Proceedings of the Eurographics Symposium on Geometry Processing. 211--221 . DOI:http:\/\/dx.doi.org\/10.2312\/SGP\/SGP06\/ 211 - 221 10.2312\/SGP Gokul Varadhan, Shankar Krishnan, Liangjun Zhang, and Dinesh Manocha. 2006. Reliable implicit surface polygonization using visibility mapping. In Proceedings of the Eurographics Symposium on Geometry Processing. 211--221. DOI:http:\/\/dx.doi.org\/10.2312\/SGP\/SGP06\/211-221"},{"key":"e_1_2_1_145_1","doi-asserted-by":"publisher","DOI":"10.1080\/10867651.1996.10487456"},{"key":"e_1_2_1_146_1","doi-asserted-by":"publisher","DOI":"10.1145\/337680.337717"},{"key":"e_1_2_1_147_1","volume-title":"Implicit Objects in Computer Graphics","author":"Velho Luiz","unstructured":"Luiz Velho , Jonas Gomes , and Luiz Henrique de Figueiredo . 2002. Implicit Objects in Computer Graphics . Springer . Luiz Velho, Jonas Gomes, and Luiz Henrique de Figueiredo. 2002. Implicit Objects in Computer Graphics. Springer."},{"key":"e_1_2_1_148_1","doi-asserted-by":"publisher","DOI":"10.1111\/1467-8659.00532"},{"key":"e_1_2_1_149_1","doi-asserted-by":"publisher","DOI":"10.1145\/192161.192227"},{"key":"e_1_2_1_151_1","volume-title":"Proceedings of Implicit Surfaces \u201998","author":"Wyvill Brian","year":"1998","unstructured":"Brian Wyvill , Eric Galin , and Andrew Guy . 1998 . The blob tree, warping, blending and Boolean operations in an implicit surface modeling system . In Proceedings of Implicit Surfaces \u201998 . Brian Wyvill, Eric Galin, and Andrew Guy. 1998. The blob tree, warping, blending and Boolean operations in an implicit surface modeling system. In Proceedings of Implicit Surfaces \u201998."},{"key":"e_1_2_1_152_1","doi-asserted-by":"publisher","DOI":"10.1142\/S0218654396000142"},{"key":"e_1_2_1_153_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01900346"},{"key":"e_1_2_1_154_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cag.2008.09.007"},{"key":"e_1_2_1_155_1","doi-asserted-by":"publisher","DOI":"10.5555\/795681.797476"},{"key":"e_1_2_1_156_1","doi-asserted-by":"publisher","DOI":"10.1109\/ICAT.2006.62"}],"container-title":["ACM Computing Surveys"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2732197","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/2732197","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T19:04:09Z","timestamp":1750273449000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2732197"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,5,26]]},"references-count":146,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2015,7,21]]}},"alternative-id":["10.1145\/2732197"],"URL":"https:\/\/doi.org\/10.1145\/2732197","relation":{},"ISSN":["0360-0300","1557-7341"],"issn-type":[{"value":"0360-0300","type":"print"},{"value":"1557-7341","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,5,26]]},"assertion":[{"value":"2013-12-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2015-02-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2015-05-26","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}