Isotopic Reconstruction of Surfaces with Boundaries
We present an algorithm for the reconstruction of a surface with boundaries (including a non‐orientable one) in three dimensions from a sufficiently dense sample. It is guaranteed that the output is isotopic to the unknown sampled surface. No previously known algorithm guarantees isotopic or homeomo...
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| Published in | Computer graphics forum Vol. 28; no. 5; pp. 1371 - 1382 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Oxford, UK
Blackwell Publishing Ltd
01.07.2009
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0167-7055 1467-8659 |
| DOI | 10.1111/j.1467-8659.2009.01514.x |
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| Abstract | We present an algorithm for the reconstruction of a surface with boundaries (including a non‐orientable one) in three dimensions from a sufficiently dense sample. It is guaranteed that the output is isotopic to the unknown sampled surface. No previously known algorithm guarantees isotopic or homeomorphic reconstruction of surfaces with boundaries. Our algorithm is surprisingly simple. It ‘peels’ slivers greedily from an α‐complex of a sample of the surface. No other post‐processing is necessary. We provide several experimental results from an implementation of our basic algorithm and also a modified version of it. |
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| AbstractList | We present an algorithm for the reconstruction of a surface with boundaries (including a non‐orientable one) in three dimensions from a sufficiently dense sample. It is guaranteed that the output is isotopic to the unknown sampled surface. No previously known algorithm guarantees isotopic or homeomorphic reconstruction of surfaces with boundaries. Our algorithm is surprisingly simple. It ‘peels’ slivers greedily from an α‐complex of a sample of the surface. No other post‐processing is necessary. We provide several experimental results from an implementation of our basic algorithm and also a modified version of it. We present an algorithm for the reconstruction of a surface with boundaries (including a non-orientable one) in three dimensions from a sufficiently dense sample. It is guaranteed that the output is isotopic to the unknown sampled surface. No previously known algorithm guarantees isotopic or homeomorphic reconstruction of surfaces with boundaries. Our algorithm is surprisingly simple. It 'peels' slivers greedily from an a-complex of a sample of the surface. No other post-processing is necessary. We provide several experimental results from an implementation of our basic algorithm and also a modified version of it. We present an algorithm for the reconstruction of a surface with boundaries (including a non-orientable one) in three dimensions from a sufficiently dense sample. It is guaranteed that the output is isotopic to the unknown sampled surface. No previously known algorithm guarantees isotopic or homeomorphic reconstruction of surfaces with boundaries. Our algorithm is surprisingly simple. It peels slivers greedily from an α-complex of a sample of the surface. No other post-processing is necessary. We provide several experimental results from an implementation of our basic algorithm and also a modified version of it. [PUBLICATION ABSTRACT] |
| Author | Ramos, Edgar A. Li, Kuiyu Dey, Tamal K. Wenger, Rephael |
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| Copyright | 2009 The Author(s) Journal compilation © 2009 The Eurographics Association and Blackwell Publishing Ltd. 2009 The Eurographics Association and Blackwell Publishing Ltd. |
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| References | Edelsbrunner H.: The union of balls and its dual shape. Discr. Comput. Geom. 13 (1995), 415-440. Amenta N., Bern M.: Surface reconstruction by voronoi filtering. Discr. Comput. Geom. 22 (1999), 481-504. Amenta N., Choi S., Dey T. K., Leekha N.: A simple algorithm for homeomorphic surface reconstruction. Internat. J. Comput. Geom. & Applications 12 (2002), 125-141. Niyogi P., Smale S., Weinberger S.: Finding the homology of sub-manifolds with high confidence from random samples. Discr. Comput. Geom. 39 (2008), 419-441. 22 12 13 39 2001 2000 2008 2007 2006 2005 1994 2003 1992 2002 e_1_2_8_16_2 Edelsbrunner H. (e_1_2_8_12_2) 2003 e_1_2_8_17_2 e_1_2_8_18_2 Niyogi P. (e_1_2_8_20_2); 39 e_1_2_8_19_2 e_1_2_8_23_2 e_1_2_8_13_2 e_1_2_8_14_2 e_1_2_8_15_2 Amenta N. (e_1_2_8_2_2); 22 e_1_2_8_4_2 Edelsbrunner H. (e_1_2_8_11_2); 13 e_1_2_8_6_2 Dey T. K. (e_1_2_8_9_2) 2007 e_1_2_8_5_2 e_1_2_8_8_2 Amenta N. (e_1_2_8_3_2); 12 e_1_2_8_7_2 e_1_2_8_10_2 e_1_2_8_21_2 e_1_2_8_22_2 |
| References_xml | – reference: Edelsbrunner H.: The union of balls and its dual shape. Discr. Comput. Geom. 13 (1995), 415-440. – reference: Niyogi P., Smale S., Weinberger S.: Finding the homology of sub-manifolds with high confidence from random samples. Discr. Comput. Geom. 39 (2008), 419-441. – reference: Amenta N., Choi S., Dey T. K., Leekha N.: A simple algorithm for homeomorphic surface reconstruction. Internat. J. Comput. Geom. & Applications 12 (2002), 125-141. – reference: Amenta N., Bern M.: Surface reconstruction by voronoi filtering. Discr. Comput. Geom. 22 (1999), 481-504. – start-page: 223 year: 2000 end-page: 232 – start-page: 263 year: 2005 end-page: 271 – start-page: 285 year: 1994 end-page: 292 – start-page: 415 year: 2005 end-page: 422 – start-page: 379 year: 2003 end-page: 404 – start-page: 319 year: 2006 end-page: 326 – start-page: 463 year: 2003 end-page: 470 – start-page: 257 year: 2001 end-page: 263 – year: 2007 – start-page: 641 year: 2003 end-page: 650 – start-page: 39 year: 2007 end-page: 48 – start-page: 781 year: 2002 end-page: 790 – start-page: 61 year: 2006 end-page: 70 – start-page: 71 year: 1992 end-page: 78 – volume: 13 start-page: 415 issue: 1995 end-page: 440 article-title: The union of balls and its dual shape publication-title: Discr. Comput. Geom. – start-page: 3 year: 2008 end-page: 12 – volume: 39 start-page: 419 issue: 2008 end-page: 441 article-title: Finding the homology of sub‐manifolds with high confidence from random samples publication-title: Discr. Comput. Geom. – volume: 22 start-page: 481 issue: 1999 end-page: 504 article-title: Surface reconstruction by voronoi filtering publication-title: Discr. Comput. Geom. – start-page: 363 year: 2002 end-page: 371 – volume: 12 start-page: 125 issue: 2002 end-page: 141 article-title: A simple algorithm for homeomorphic surface reconstruction publication-title: Internat. J. Comput. Geom. & Applications – start-page: 544 year: 2005 end-page: 552 – start-page: 1018 year: 2005 end-page: 1027 – ident: e_1_2_8_17_2 doi: 10.1145/142920.134011 – ident: e_1_2_8_6_2 – ident: e_1_2_8_19_2 – ident: e_1_2_8_8_2 – ident: e_1_2_8_10_2 doi: 10.1145/378583.378682 – ident: e_1_2_8_5_2 doi: 10.1145/336154.336208 – ident: e_1_2_8_15_2 – ident: e_1_2_8_16_2 doi: 10.1111/1467-8659.00596 – volume: 12 start-page: 125 issue: 2002 ident: e_1_2_8_3_2 article-title: A simple algorithm for homeomorphic surface reconstruction publication-title: Internat. J. Comput. Geom. & Applications – ident: e_1_2_8_22_2 doi: 10.1145/882262.882319 – ident: e_1_2_8_7_2 – volume: 13 start-page: 415 issue: 1995 ident: e_1_2_8_11_2 article-title: The union of balls and its dual shape publication-title: Discr. Comput. Geom. – start-page: 379 volume-title: Ricky Pollack and Eli Goodman Festschrift year: 2003 ident: e_1_2_8_12_2 doi: 10.1007/978-3-642-55566-4_17 – ident: e_1_2_8_14_2 doi: 10.1145/1073204.1073227 – volume: 22 start-page: 481 issue: 1999 ident: e_1_2_8_2_2 article-title: Surface reconstruction by voronoi filtering publication-title: Discr. Comput. Geom. – ident: e_1_2_8_21_2 doi: 10.1145/882262.882293 – volume: 39 start-page: 419 issue: 2008 ident: e_1_2_8_20_2 article-title: Finding the homology of sub‐manifolds with high confidence from random samples publication-title: Discr. Comput. Geom. – ident: e_1_2_8_23_2 – ident: e_1_2_8_4_2 – volume-title: Cambridge University Press year: 2007 ident: e_1_2_8_9_2 – ident: e_1_2_8_13_2 – ident: e_1_2_8_18_2 |
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| Snippet | We present an algorithm for the reconstruction of a surface with boundaries (including a non‐orientable one) in three dimensions from a sufficiently dense... We present an algorithm for the reconstruction of a surface with boundaries (including a non-orientable one) in three dimensions from a sufficiently dense... |
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| SubjectTerms | Algorithms Computer graphics Computer programming I.3.3 [Computer Graphics]: Surface Reconstruction Sampling Studies |
| Title | Isotopic Reconstruction of Surfaces with Boundaries |
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