Manifold Homotopy via the Flow Complex
It is known that the critical points of the distance function induced by a dense sample P of a submanifold Σ of ℝn are distributed into two groups, one lying close to Σ itself, called the shallow, and the other close to medial axis of Σ, called deep critical points. We prove that under (uniform) sam...
Saved in:
| Published in: | Computer graphics forum Vol. 28; no. 5; pp. 1361 - 1370 |
|---|---|
| Main Author: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
Oxford, UK
Blackwell Publishing Ltd
01.07.2009
|
| Subjects: | |
| ISSN: | 0167-7055, 1467-8659 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | It is known that the critical points of the distance function induced by a dense sample P of a submanifold Σ of ℝn are distributed into two groups, one lying close to Σ itself, called the shallow, and the other close to medial axis of Σ, called deep critical points. We prove that under (uniform) sampling assumption, the union of stable manifolds of the shallow critical points have the same homotopy type as Σ itself and the union of the stable manifolds of the deep critical points have the homotopy type of the complement of Σ. The separation of critical points under uniform sampling entails a separation in terms of distance of critical points to the sample. This means that if a given sample is dense enough with respect to two or more submanifolds of ℝn, the homotopy types of all such submanifolds together with those of their complements are captured as unions of stable manifolds of shallow versus those of deep critical points, in a filtration of the flow complex based on the distance of critical points to the sample. This results in an algorithm for homotopic manifold reconstruction when the target dimension is unknown. |
|---|---|
| AbstractList | It is known that the critical points of the distance function induced by a dense sample P of a submanifold S of Rn are distributed into two groups, one lying close to S itself, called the shallow, and the other close to medial axis of S, called deep critical points. We prove that under (uniform) sampling assumption, the union of stable manifolds of the shallow critical points have the same homotopy type as S itself and the union of the stable manifolds of the deep critical points have the homotopy type of the complement of S. The separation of critical points under uniform sampling entails a separation in terms of distance of critical points to the sample. This means that if a given sample is dense enough with respect to two or more submanifolds of Rn, the homotopy types of all such submanifolds together with those of their complements are captured as unions of stable manifolds of shallow versus those of deep critical points, in a filtration of the flow complex based on the distance of critical points to the sample. This results in an algorithm for homotopic manifold reconstruction when the target dimension is unknown. It is known that the critical points of the distance function induced by a dense sample P of a submanifold Σ of ℝn are distributed into two groups, one lying close to Σ itself, called the shallow, and the other close to medial axis of Σ, called deep critical points. We prove that under (uniform) sampling assumption, the union of stable manifolds of the shallow critical points have the same homotopy type as Σ itself and the union of the stable manifolds of the deep critical points have the homotopy type of the complement of Σ. The separation of critical points under uniform sampling entails a separation in terms of distance of critical points to the sample. This means that if a given sample is dense enough with respect to two or more submanifolds of ℝn, the homotopy types of all such submanifolds together with those of their complements are captured as unions of stable manifolds of shallow versus those of deep critical points, in a filtration of the flow complex based on the distance of critical points to the sample. This results in an algorithm for homotopic manifold reconstruction when the target dimension is unknown. It is known that the critical points of the distance function induced by a dense sample P of a submanifold Σ of ℝ n are distributed into two groups, one lying close to Σ itself, called the shallow , and the other close to medial axis of Σ, called deep critical points. We prove that under (uniform) sampling assumption, the union of stable manifolds of the shallow critical points have the same homotopy type as Σ itself and the union of the stable manifolds of the deep critical points have the homotopy type of the complement of Σ. The separation of critical points under uniform sampling entails a separation in terms of distance of critical points to the sample. This means that if a given sample is dense enough with respect to two or more submanifolds of ℝ n , the homotopy types of all such submanifolds together with those of their complements are captured as unions of stable manifolds of shallow versus those of deep critical points, in a filtration of the flow complex based on the distance of critical points to the sample. This results in an algorithm for homotopic manifold reconstruction when the target dimension is unknown. It is known that the critical points of the distance function induced by a dense sample P of a submanifold ? of ?n are distributed into two groups, one lying close to ? itself, called the shallow, and the other close to medial axis of ?, called deep critical points. We prove that under (uniform) sampling assumption, the union of stable manifolds of the shallow critical points have the same homotopy type as ? itself and the union of the stable manifolds of the deep critical points have the homotopy type of the complement of ?. The separation of critical points under uniform sampling entails a separation in terms of distance of critical points to the sample. This means that if a given sample is dense enough with respect to two or more submanifolds of ?n, the homotopy types of all such submanifolds together with those of their complements are captured as unions of stable manifolds of shallow versus those of deep critical points, in a filtration of the flow complex based on the distance of critical points to the sample. This results in an algorithm for homotopic manifold reconstruction when the target dimension is unknown. [PUBLICATION ABSTRACT] |
| Author | Sadri, Bardia |
| Author_xml | – sequence: 1 givenname: Bardia surname: Sadri fullname: Sadri, Bardia organization: Department of Computer Science, University of Toronto, Toronto, Ontario, Canada |
| BookMark | eNqNkM1OwzAQhC1UJErhHSIOvSXYsePYB5Cgoi0SPxdQJS4rk2yESxqXOIX27Uko6qGn7mVX8nzj0ZySXuUqJCRgNGLtXM4jJmQaKpnoKKZUR5QljEfrI9LfPfRIn7L2TmmSnJBT7-eUUpHKpE-Gj6ayhSvzYOoWrnHLTfBtTdB8YDAu3U8wcotlieszclyY0uP5_x6Q1_Hdy2gaPjxP7kc3D2EmUs1DwzFGUwga01xLbpShsXgvUHORS6UKyXKWaYEccyVYkreBM0kpYpyw1IiCD8hw67us3dcKfQML6zMsS1OhW3ngQimdCtUKL_aEc7eqqzYbMC2kYrrNMyBqK8pq532NBSxruzD1BhiFrj2YQ1cSdCVB1x78tQfrFr3eQzPbmMa6qqmNLQ8xuNoa_NgSNwd_DKPJuLtaPtzy1je43vGm_gSZ8jSB2dMEptPZWxzfUrjlv5Ghl88 |
| CitedBy_id | crossref_primary_10_1016_j_cag_2013_05_016 |
| Cites_doi | 10.1007/PL00009475 10.1007/978-3-540-33259-6_6 10.1145/1137856.1137876 10.1016/S0925-7721(01)00048-7 10.1007/BF02574053 10.1142/S0218195902000773 10.1145/357346.357349 10.1145/1137856.1137906 10.1145/1377676.1377719 10.1016/S0925-7721(01)00017-7 10.1016/S0304-3975(02)00691-6 10.1007/s00454-006-1250-7 10.1090/pspum/054.3/1216630 10.1006/gmip.1998.0465 10.1145/142920.134011 10.1016/j.comgeo.2007.05.005 10.1016/j.cad.2004.01.011 10.1111/1467-8659.00596 |
| ContentType | Journal Article |
| Copyright | 2009 The Author(s) Journal compilation © 2009 The Eurographics Association and Blackwell Publishing Ltd. 2009 The Eurographics Association and Blackwell Publishing Ltd. |
| Copyright_xml | – notice: 2009 The Author(s) Journal compilation © 2009 The Eurographics Association and Blackwell Publishing Ltd. – notice: 2009 The Eurographics Association and Blackwell Publishing Ltd. |
| DBID | BSCLL AAYXX CITATION 7SC 8FD JQ2 L7M L~C L~D F28 FR3 |
| DOI | 10.1111/j.1467-8659.2009.01513.x |
| DatabaseName | Istex CrossRef Computer and Information Systems Abstracts Technology Research Database ProQuest Computer Science Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional ANTE: Abstracts in New Technology & Engineering Engineering Research Database |
| DatabaseTitle | CrossRef Computer and Information Systems Abstracts Technology Research Database Computer and Information Systems Abstracts – Academic Advanced Technologies Database with Aerospace ProQuest Computer Science Collection Computer and Information Systems Abstracts Professional Engineering Research Database ANTE: Abstracts in New Technology & Engineering |
| DatabaseTitleList | Technology Research Database CrossRef Computer and Information Systems Abstracts |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering |
| EISSN | 1467-8659 |
| EndPage | 1370 |
| ExternalDocumentID | 1852597771 10_1111_j_1467_8659_2009_01513_x CGF1513 ark_67375_WNG_HHWZ22B0_B |
| Genre | article Feature |
| GroupedDBID | .3N .4S .DC .GA .Y3 05W 0R~ 10A 15B 1OB 1OC 29F 31~ 33P 3SF 4.4 50Y 50Z 51W 51X 52M 52N 52O 52P 52S 52T 52U 52W 52X 5GY 5HH 5LA 5VS 66C 6J9 702 7PT 8-0 8-1 8-3 8-4 8-5 8UM 8VB 930 A03 AAESR AAEVG AAHQN AAMMB AAMNL AANHP AANLZ AAONW AASGY AAXRX AAYCA AAZKR ABCQN ABCUV ABDBF ABDPE ABEML ABPVW ACAHQ ACBWZ ACCZN ACFBH ACGFS ACPOU ACRPL ACSCC ACUHS ACXBN ACXQS ACYXJ ADBBV ADEOM ADIZJ ADKYN ADMGS ADMLS ADNMO ADOZA ADXAS ADZMN AEFGJ AEGXH AEIGN AEIMD AEMOZ AENEX AEUYR AEYWJ AFBPY AFEBI AFFNX AFFPM AFGKR AFWVQ AFZJQ AGHNM AGQPQ AGXDD AGYGG AHBTC AHEFC AHQJS AIDQK AIDYY AIQQE AITYG AIURR AJXKR AKVCP ALAGY ALMA_UNASSIGNED_HOLDINGS ALVPJ AMBMR AMYDB ARCSS ASPBG ATUGU AUFTA AVWKF AZBYB AZFZN AZVAB BAFTC BDRZF BFHJK BHBCM BMNLL BMXJE BNHUX BROTX BRXPI BSCLL BY8 CAG COF CS3 CWDTD D-E D-F DCZOG DPXWK DR2 DRFUL DRSTM DU5 EAD EAP EBA EBO EBR EBS EBU EDO EJD EMK EST ESX F00 F01 F04 F5P FEDTE FZ0 G-S G.N GODZA H.T H.X HF~ HGLYW HVGLF HZI HZ~ I-F IHE IX1 J0M K1G K48 LATKE LC2 LC3 LEEKS LH4 LITHE LOXES LP6 LP7 LUTES LW6 LYRES MEWTI MK4 MRFUL MRSTM MSFUL MSSTM MXFUL MXSTM N04 N05 N9A NF~ O66 O9- OIG P2W P2X P4D PALCI PQQKQ Q.N Q11 QB0 QWB R.K RDJ RIWAO RJQFR ROL RX1 SAMSI SUPJJ TH9 TN5 TUS UB1 V8K W8V W99 WBKPD WIH WIK WOHZO WQJ WXSBR WYISQ WZISG XG1 ZL0 ZZTAW ~IA ~IF ~WT AAHHS ACCFJ ADZOD AEEZP AEQDE AEUQT AFPWT AIWBW AJBDE ALUQN WRC AAYXX CITATION O8X 7SC 8FD JQ2 L7M L~C L~D F28 FR3 |
| ID | FETCH-LOGICAL-c4793-a3e2eaf4020d963a8a024bfe934d688f61d1c94e3ed8415d200c600ee2517a4f3 |
| IEDL.DBID | DRFUL |
| ISICitedReferencesCount | 2 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000268597500012&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0167-7055 |
| IngestDate | Thu Sep 04 16:23:31 EDT 2025 Fri Jul 25 02:11:18 EDT 2025 Sat Nov 29 03:41:04 EST 2025 Tue Nov 18 22:36:40 EST 2025 Wed Jan 22 17:03:58 EST 2025 Tue Nov 11 03:32:10 EST 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 5 |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c4793-a3e2eaf4020d963a8a024bfe934d688f61d1c94e3ed8415d200c600ee2517a4f3 |
| Notes | ArticleID:CGF1513 istex:DC89D7D061AFF38722F73EFB3856292DF81E14D3 ark:/67375/WNG-HHWZ22B0-B SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-2 content type line 23 |
| PQID | 194681979 |
| PQPubID | 30877 |
| PageCount | 10 |
| ParticipantIDs | proquest_miscellaneous_34889748 proquest_journals_194681979 crossref_primary_10_1111_j_1467_8659_2009_01513_x crossref_citationtrail_10_1111_j_1467_8659_2009_01513_x wiley_primary_10_1111_j_1467_8659_2009_01513_x_CGF1513 istex_primary_ark_67375_WNG_HHWZ22B0_B |
| PublicationCentury | 2000 |
| PublicationDate | July 2009 |
| PublicationDateYYYYMMDD | 2009-07-01 |
| PublicationDate_xml | – month: 07 year: 2009 text: July 2009 |
| PublicationDecade | 2000 |
| PublicationPlace | Oxford, UK |
| PublicationPlace_xml | – name: Oxford, UK – name: Oxford |
| PublicationTitle | Computer graphics forum |
| PublicationYear | 2009 |
| Publisher | Blackwell Publishing Ltd |
| Publisher_xml | – name: Blackwell Publishing Ltd |
| References | Nina Amenta, Sunghee Choi, Tamal K. Dey, and N. Leekha. A simple algorithm for homeomorphic surface reconstruction. Internat. J. Comput. Geom. Appl., 12(1-2):125-141, 2002. Allen Hatcher. Algebraic Topology. Cambridge University Press, 2001. Nina Amenta, Marshall W. Bern, and David Eppstein. The crust and the β-skeleton: Combinatorial curve reconstruction. Graphical Models and Processing, 60(2):125-135, 1998. Kevin Buchin, Tamal K. Dey, Joachim Giesen, and Matthias John Recursive geometry of the flow complex and topology of the flow complex filtration. Comput. Geom. Theory Appl., 40:115-157, 2008. H. Edelsbrunner. The union of balls and its dual shape. Discrete Comput. Geom., 13:415-440, 1995. Herbert Edelsbrunner. Surface reconstruction by wrapping finite point sets in space. Discrete & Computational Geometry, 32:231-244, 2004. André Lieutier. Any bounded open subset of ℝn has the same homotopy type as its medial axis. Computer-Aided Design, 36(11):1029-1046, 2004. Nina Amenta, Sunghee Choi, and Ravi Krishna Kolluri. The power crust, unions of balls, and the medial axis transform. Comput. Geom. Theory Appl., 19(2-3):127-153, 2001. Jean-Daniel Boissonnat. Geometric structures for three-dimensional shape representation. ACM Trans. Graph., 3(4):266-286, 1984. Joachim Giesen and Matthias John. Surface reconstruction based on a dynamical system. Computer Graphics Forume, 21:363-371, 2002. Nina Amenta, Thomas J. Peters, and Alexander Russell. Computational topology: Ambient isotopic approximation of 2-manifolds. Theo. Comp. Sci., 305(1-3):3-15, 2003. Karl Grove. Critical point theory for distance functions. Symposia in Pure Mathematics, 54(3):357-385, 1993. Nina Amenta and Marshall W. Bern. Surface reconstruction by Voronoi filtering. Discrete Comput. Geom., 22:481-504, 1999. Jean-Daniel Boissonnat and Frédéric Cazals. Smooth surface reconstruction via natural neighbour interpolation of distance functions. Comput. Geom. Theory Appl., 22(1-3):185-203, 2002. 2004; 32 2003; 305 2001 1984; 3 2002; 12 1995; 13 2004; 36 1993; 54 2002; 21 2002; 22 2001; 19 2008 1999; 22 2007 2006 2005 2003 1992 1998; 60 2008; 40 1999 e_1_2_6_30_2 e_1_2_6_18_2 e_1_2_6_19_2 e_1_2_6_12_2 e_1_2_6_13_2 e_1_2_6_10_2 Hatcher Allen (e_1_2_6_27_2) 2001 e_1_2_6_11_2 e_1_2_6_32_2 e_1_2_6_16_2 e_1_2_6_17_2 e_1_2_6_14_2 e_1_2_6_15_2 Edelsbrunner Herbert (e_1_2_6_21_2) 2004; 32 e_1_2_6_20_2 e_1_2_6_8_2 e_1_2_6_7_2 e_1_2_6_9_2 e_1_2_6_29_2 e_1_2_6_4_2 e_1_2_6_3_2 e_1_2_6_6_2 e_1_2_6_5_2 Petrunin A. (e_1_2_6_31_2) 2007 e_1_2_6_24_2 e_1_2_6_23_2 e_1_2_6_2_2 e_1_2_6_22_2 Siersma Dirk (e_1_2_6_33_2) 1999 e_1_2_6_28_2 e_1_2_6_26_2 e_1_2_6_25_2 |
| References_xml | – reference: Herbert Edelsbrunner. Surface reconstruction by wrapping finite point sets in space. Discrete & Computational Geometry, 32:231-244, 2004. – reference: Karl Grove. Critical point theory for distance functions. Symposia in Pure Mathematics, 54(3):357-385, 1993. – reference: Nina Amenta, Thomas J. Peters, and Alexander Russell. Computational topology: Ambient isotopic approximation of 2-manifolds. Theo. Comp. Sci., 305(1-3):3-15, 2003. – reference: Kevin Buchin, Tamal K. Dey, Joachim Giesen, and Matthias John Recursive geometry of the flow complex and topology of the flow complex filtration. Comput. Geom. Theory Appl., 40:115-157, 2008. – reference: H. Edelsbrunner. The union of balls and its dual shape. Discrete Comput. Geom., 13:415-440, 1995. – reference: Nina Amenta, Marshall W. Bern, and David Eppstein. The crust and the β-skeleton: Combinatorial curve reconstruction. Graphical Models and Processing, 60(2):125-135, 1998. – reference: Allen Hatcher. Algebraic Topology. Cambridge University Press, 2001. – reference: Joachim Giesen and Matthias John. Surface reconstruction based on a dynamical system. Computer Graphics Forume, 21:363-371, 2002. – reference: Jean-Daniel Boissonnat and Frédéric Cazals. Smooth surface reconstruction via natural neighbour interpolation of distance functions. Comput. Geom. Theory Appl., 22(1-3):185-203, 2002. – reference: Jean-Daniel Boissonnat. Geometric structures for three-dimensional shape representation. ACM Trans. Graph., 3(4):266-286, 1984. – reference: Nina Amenta, Sunghee Choi, Tamal K. Dey, and N. Leekha. A simple algorithm for homeomorphic surface reconstruction. Internat. J. Comput. Geom. Appl., 12(1-2):125-141, 2002. – reference: André Lieutier. Any bounded open subset of ℝn has the same homotopy type as its medial axis. Computer-Aided Design, 36(11):1029-1046, 2004. – reference: Nina Amenta and Marshall W. Bern. Surface reconstruction by Voronoi filtering. Discrete Comput. Geom., 22:481-504, 1999. – reference: Nina Amenta, Sunghee Choi, and Ravi Krishna Kolluri. The power crust, unions of balls, and the medial axis transform. Comput. Geom. Theory Appl., 19(2-3):127-153, 2001. – volume: 54 start-page: 357 issue: 3 year: 1993 end-page: 385 article-title: Critical point theory for distance functions publication-title: Symposia in Pure Mathematics – volume: 3 start-page: 266 issue: 4 year: 1984 end-page: 286 article-title: Geometric structures for three‐dimensional shape representation publication-title: ACM Trans. Graph. – volume: 22 start-page: 185 issue: 1‐3 year: 2002 end-page: 203 article-title: Smooth surface reconstruction via natural neighbour interpolation of distance functions publication-title: Comput. Geom. Theory Appl. – volume: 60 start-page: 125 issue: 2 year: 1998 end-page: 135 article-title: The crust and the β‐skeleton: Combinatorial curve reconstruction publication-title: Graphical Models and Processing – start-page: 319 year: 2006 end-page: 326 – start-page: 1076 year: 2007 end-page: 1085 – volume: 13 start-page: 415 year: 1995 end-page: 440 article-title: The union of balls and its dual shape publication-title: Discrete Comput. Geom. – start-page: 112 year: 2006 end-page: 118 – year: 2001 – year: 2007 – start-page: 337 year: 2006 end-page: 346 – volume: 19 start-page: 127 issue: 2‐3 year: 2001 end-page: 153 article-title: The power crust, unions of balls, and the medial axis transform publication-title: Comput. Geom. Theory Appl. – start-page: 187 year: 1999 end-page: 208 – volume: 12 start-page: 125 issue: 1‐2 year: 2002 end-page: 141 article-title: A simple algorithm for homeomorphic surface reconstruction publication-title: Internat. J. Comput. Geom. Appl. – start-page: 71 year: 1992 end-page: 78 – start-page: 270 year: 2005 end-page: 273 – start-page: 493 year: 2003 end-page: 502 – volume: 305 start-page: 3 issue: 1‐3 year: 2003 end-page: 15 article-title: Computational topology: Ambient isotopic approximation of 2‐manifolds publication-title: Theo. Comp. Sci. – start-page: 232 year: 2008 end-page: 241 – volume: 32 start-page: 231 year: 2004 end-page: 244 article-title: Surface reconstruction by wrapping finite point sets in space publication-title: Discrete & Computational Geometry – year: 2006 – volume: 40 start-page: 115 year: 2008 end-page: 157 article-title: Recursive geometry of the flow complex and topology of the flow complex filtration publication-title: Comput. Geom. Theory Appl. – start-page: 218 year: 2005 end-page: 227 – volume: 21 start-page: 363 year: 2002 end-page: 371 article-title: Surface reconstruction based on a dynamical system publication-title: Computer Graphics Forume – volume: 36 start-page: 1029 issue: 11 year: 2004 end-page: 1046 article-title: Any bounded open subset of ℝ has the same homotopy type as its medial axis publication-title: Computer-Aided Design – start-page: 285 year: 2003 end-page: 294 – start-page: 327 year: 2006 end-page: 336 – volume: 22 start-page: 481 year: 1999 end-page: 504 article-title: Surface reconstruction by Voronoi filtering publication-title: Discrete Comput. Geom. – ident: e_1_2_6_19_2 – ident: e_1_2_6_2_2 doi: 10.1007/PL00009475 – ident: e_1_2_6_10_2 – ident: e_1_2_6_15_2 doi: 10.1007/978-3-540-33259-6_6 – ident: e_1_2_6_24_2 – ident: e_1_2_6_16_2 doi: 10.1145/1137856.1137876 – ident: e_1_2_6_13_2 – ident: e_1_2_6_3_2 – ident: e_1_2_6_32_2 – ident: e_1_2_6_8_2 doi: 10.1016/S0925-7721(01)00048-7 – ident: e_1_2_6_20_2 doi: 10.1007/BF02574053 – ident: e_1_2_6_5_2 doi: 10.1142/S0218195902000773 – ident: e_1_2_6_12_2 doi: 10.1145/357346.357349 – ident: e_1_2_6_11_2 doi: 10.1145/1137856.1137906 – ident: e_1_2_6_17_2 doi: 10.1145/1377676.1377719 – ident: e_1_2_6_6_2 doi: 10.1016/S0925-7721(01)00017-7 – ident: e_1_2_6_7_2 doi: 10.1016/S0304-3975(02)00691-6 – ident: e_1_2_6_30_2 doi: 10.1007/s00454-006-1250-7 – volume-title: Surveys in Differential Geometry, volume XI: Metric and Comparison Geometry year: 2007 ident: e_1_2_6_31_2 – ident: e_1_2_6_26_2 – ident: e_1_2_6_23_2 – ident: e_1_2_6_18_2 – ident: e_1_2_6_25_2 doi: 10.1090/pspum/054.3/1216630 – ident: e_1_2_6_4_2 doi: 10.1006/gmip.1998.0465 – volume: 32 start-page: 231 year: 2004 ident: e_1_2_6_21_2 article-title: Surface reconstruction by wrapping finite point sets in space publication-title: Discrete & Computational Geometry – volume-title: Algebraic Topology year: 2001 ident: e_1_2_6_27_2 – ident: e_1_2_6_28_2 doi: 10.1145/142920.134011 – ident: e_1_2_6_9_2 doi: 10.1016/j.comgeo.2007.05.005 – start-page: 187 volume-title: Geometry in Present Day Science year: 1999 ident: e_1_2_6_33_2 – ident: e_1_2_6_14_2 – ident: e_1_2_6_29_2 doi: 10.1016/j.cad.2004.01.011 – ident: e_1_2_6_22_2 doi: 10.1111/1467-8659.00596 |
| SSID | ssj0004765 |
| Score | 1.8801924 |
| Snippet | It is known that the critical points of the distance function induced by a dense sample P of a submanifold Σ of ℝn are distributed into two groups, one lying... It is known that the critical points of the distance function induced by a dense sample P of a submanifold Σ of ℝ n are distributed into two groups, one lying... It is known that the critical points of the distance function induced by a dense sample P of a submanifold ? of ?n are distributed into two groups, one lying... It is known that the critical points of the distance function induced by a dense sample P of a submanifold S of Rn are distributed into two groups, one lying... |
| SourceID | proquest crossref wiley istex |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 1361 |
| SubjectTerms | Algorithms Computer graphics F.2.2 [Theory of Computation]: Nonnumerical Algorithms and Prolems-Geometric Problems and Computation Geometry Sampling Studies |
| Title | Manifold Homotopy via the Flow Complex |
| URI | https://api.istex.fr/ark:/67375/WNG-HHWZ22B0-B/fulltext.pdf https://onlinelibrary.wiley.com/doi/abs/10.1111%2Fj.1467-8659.2009.01513.x https://www.proquest.com/docview/194681979 https://www.proquest.com/docview/34889748 |
| Volume | 28 |
| WOSCitedRecordID | wos000268597500012&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVWIB databaseName: Wiley Online Library Full Collection 2020 customDbUrl: eissn: 1467-8659 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0004765 issn: 0167-7055 databaseCode: DRFUL dateStart: 19970101 isFulltext: true titleUrlDefault: https://onlinelibrary.wiley.com providerName: Wiley-Blackwell |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1LT8MwDLbQxgEOvBFlPHpA3IroY2ly5FV2gAkhEIhLlKaJNDG10wZj_HvsrhtMcECIW6XKVerY8ZfY-QxwgGajfKGtFzQpzaht7ClEDV5AfHccY3zIVdlsIm63-eOjuKnqn-guzJgfYnrgRp5Rrtfk4CodfHdyzpqiop3E4BUeIZ6sB2jGUQ3q57fJ_dXnLcmYNSdM38QhM1vX8-O3ZoJVnfQ-mkGiX_FsGZCS5f_8lRVYqmCpezK2o1WYM_kaLH4hK1yHw2uVd2zRzdwWVfAVvXd32FEuAkg36RZvLq0sXTPagPvk4u6s5VVdFjxNp2qeCk1glKV9ZIbeqLjCsJ1aI8IoY5xb5me-FpEJTcYx2mc4QI0oyRgiO1ORDTehlhe52QJXINpiKT9mRsfE05ZSExyTZYFOrWUqdSCeqFPqioKcOmF05cxWJJakCWqQKWSpCTlywJ9K9sY0HL-QOSxnbCqg-s9UxhY35UP7UrZaD09BcHosTx1oTKZUVh48kL6IGKKlWDiwP32Lrkf5FJWb4nUgQ1z8cDvGHWDl7P56ZPLsMqGn7b8KNmBhnNWisuEdqL30X80uzOvhS2fQ36sM_wNHgPwB |
| linkProvider | Wiley-Blackwell |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV3fT9swED6hFgn2sPFTyxiQh4m3IPLLsR9pIQRRqmkCgXixHMeWqlVJ1QLr_vvdpWmh2h7QxFuk6CLn7M_32T5_B_ANh43yhbZeENMxo7aJp5A1eAHp3XGM8SFXdbGJpN_n9_fie1MOiO7CzPQhFhtuhIx6viaA04b03yjnLBaN7iRGr_AYCWU7wlEVt6B99iO97b1ck0xYPJf6JhGZ5cSef35rKVq1yfHTJSr6mtDWESn99K7_sgEfG2Lqns5G0iasmHILPrySK9yGo2tVDmw1LNyMcviq0W_3eaBcpJBuOqx-uTS3DM10B27T85tu5jV1FjxN-2qeCk1glKWVZIF4VFxh4M6tEWFUMM4t8wtfi8iEpuAY7wtsoEaeZAzJnanIhrvQKqvSfAZXIN9iOT9hRiek1JZTGRxTFIHOrWUqdyCZ-1PqRoScamEM5dJiJJHkCSqRKWTtCTl1wF9YjmZCHG-wOaq7bGGgxj8pkS2J5V3_QmbZ3UMQdE5kx4G9eZ_KBsMT6YuIIV9KhAOHi7cIPjpRUaWpniYyxOkPF2TcAVZ375tbJrsXKT19-V_DQ1jLbq57snfZv9qD9dkZFyURf4XW4_jJ7MOqfn4cTMYHDQr-AH6wAAA |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1LT9tAEB5VBKFyKJQW4dKCD4ibEX6td49NwKQqjRACgbis1vuQIiI7SniEf8-M46RE9IBQb5assdaz--18uzv7DcAeDhsVCu2CKKVjRu2yQCFrCCLSu-MY42Ou6mITWa_Hr6_FWVMOiO7CTPUh5htuhIx6viaA26Fxr1HOWSoa3UmMXvEBEspWkgqGKG0dneeXp3-vSWYsnUl9k4jMYmLPP7-1EK1a5PjJAhV9SWjriJSv_dd_WYdPDTH1f05H0mf4YMsNWH0hV_gF9v-osu-qgfG7lMNXDZ_8h77ykUL6-aB69GluGdjJV7jMjy863aCpsxBo2lcLVGwjqxytJA3iUXGFgbtwVsSJYZw7FppQi8TG1nCM9wYbqJEnWUtyZypx8SYslVVpt8AXyLdYwQ-Z1RkptRVUBscaE-nCOaYKD7KZP6VuRMipFsZALixGMkmeoBKZQtaekBMPwrnlcCrE8Qab_brL5gZqdEuJbFkqr3onstu9uomi9qFse7A961PZYHgsQ5Ew5EuZ8GB3_hbBRycqqrTV_VjGOP3hgox7wOrufXPLZOckp6dv7zXchZWzo1ye_ur93oaP0yMuyiH-Dkt3o3v7A5b1w11_PNppQPAMBTn_bA |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Manifold+Homotopy+via+the+Flow+Complex&rft.jtitle=Computer+graphics+forum&rft.au=Sadri%2C+Bardia&rft.date=2009-07-01&rft.pub=Blackwell+Publishing+Ltd&rft.issn=0167-7055&rft.eissn=1467-8659&rft.volume=28&rft.issue=5&rft.spage=1361&rft_id=info:doi/10.1111%2Fj.1467-8659.2009.01513.x&rft.externalDBID=NO_FULL_TEXT&rft.externalDocID=1852597771 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0167-7055&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0167-7055&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0167-7055&client=summon |