Planar Minimization Diagrams via Subdivision with Applications to Anisotropic Voronoi Diagrams
Let X = {f1, …, fn} be a set of scalar functions of the form fi : ℝ2 → ℝ which satisfy some natural properties. We describe a subdivision algorithm for computing a clustered ε‐isotopic approximation of the minimization diagram of X. By exploiting soft predicates and clustering of Voronoi vertices, o...
Uložené v:
| Vydané v: | Computer graphics forum Ročník 35; číslo 5; s. 229 - 247 |
|---|---|
| Hlavní autori: | , , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Oxford
Blackwell Publishing Ltd
01.08.2016
|
| Predmet: | |
| ISSN: | 0167-7055, 1467-8659 |
| On-line prístup: | Získať plný text |
| Tagy: |
Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
|
| Abstract | Let X = {f1, …, fn} be a set of scalar functions of the form fi : ℝ2 → ℝ which satisfy some natural properties. We describe a subdivision algorithm for computing a clustered ε‐isotopic approximation of the minimization diagram of X. By exploiting soft predicates and clustering of Voronoi vertices, our algorithm is the first that can handle arbitrary degeneracies in X, and allow scalar functions which are piecewise smooth, and not necessarily semi‐algebraic.
We apply these ideas to the computation of anisotropic Voronoi diagram of polygonal sets; this is a natural generalization of anisotropic Voronoi diagrams of point sites, which extends multiplicatively weighted Voronoi diagrams. We implement a prototype of our anisotropic algorithm and provide experimental results. |
|---|---|
| AbstractList | Let X = {f
1
, …, f
n
} be a set of scalar functions of the form f
i
: ℝ
2
→ ℝ which satisfy some natural properties. We describe a subdivision algorithm for computing a clustered ε‐isotopic approximation of the minimization diagram of X. By exploiting soft predicates and clustering of Voronoi vertices, our algorithm is the first that can handle arbitrary degeneracies in X, and allow scalar functions which are piecewise smooth, and not necessarily semi‐algebraic.
We apply these ideas to the computation of anisotropic Voronoi diagram of polygonal sets; this is a natural generalization of anisotropic Voronoi diagrams of point sites, which extends multiplicatively weighted Voronoi diagrams. We implement a prototype of our anisotropic algorithm and provide experimental results. Let X = {f1, …, fn} be a set of scalar functions of the form fi : ℝ2 → ℝ which satisfy some natural properties. We describe a subdivision algorithm for computing a clustered ε‐isotopic approximation of the minimization diagram of X. By exploiting soft predicates and clustering of Voronoi vertices, our algorithm is the first that can handle arbitrary degeneracies in X, and allow scalar functions which are piecewise smooth, and not necessarily semi‐algebraic. We apply these ideas to the computation of anisotropic Voronoi diagram of polygonal sets; this is a natural generalization of anisotropic Voronoi diagrams of point sites, which extends multiplicatively weighted Voronoi diagrams. We implement a prototype of our anisotropic algorithm and provide experimental results. Let X = {f1, ..., fn} be a set of scalar functions of the form fi : 2 [arrow right] which satisfy some natural properties. We describe a subdivision algorithm for computing a clustered [epsi]-isotopic approximation of the minimization diagram of X. By exploiting soft predicates and clustering of Voronoi vertices, our algorithm is the first that can handle arbitrary degeneracies in X, and allow scalar functions which are piecewise smooth, and not necessarily semi-algebraic. We apply these ideas to the computation of anisotropic Voronoi diagram of polygonal sets; this is a natural generalization of anisotropic Voronoi diagrams of point sites, which extends multiplicatively weighted Voronoi diagrams. We implement a prototype of our anisotropic algorithm and provide experimental results. Let X = {f sub(1), ..., f sub(n)} be a set of scalar functions of the form f sub(i) : super(2) arrow right which satisfy some natural properties. We describe a subdivision algorithm for computing a clustered epsilon -isotopic approximation of the minimization diagram of X. By exploiting soft predicates and clustering of Voronoi vertices, our algorithm is the first that can handle arbitrary degeneracies in X, and allow scalar functions which are piecewise smooth, and not necessarily semi-algebraic. We apply these ideas to the computation of anisotropic Voronoi diagram of polygonal sets; this is a natural generalization of anisotropic Voronoi diagrams of point sites, which extends multiplicatively weighted Voronoi diagrams. We implement a prototype of our anisotropic algorithm and provide experimental results. |
| Author | Yap, C. Papadopoulou, E. Bennett, H. |
| Author_xml | – sequence: 1 givenname: H. surname: Bennett fullname: Bennett, H. organization: Courant Institute, NYU, New York, USA – sequence: 2 givenname: E. surname: Papadopoulou fullname: Papadopoulou, E. organization: Faculty of Informatics, USI, Lugano, Switzerland – sequence: 3 givenname: C. surname: Yap fullname: Yap, C. organization: Courant Institute, NYU, New York, USA |
| BookMark | eNp9kE9PwyAYh4nRxG168Bs08aKHOmgLtMdlumkyp4n_bhJKqb6zKxU6p356cVMPJsoFAs_vl5enizZrU2uE9gg-In711UN5RKKMZxuoQxLGw5TRbBN1MPFnjindRl3nZhjjhDPaQfeXlaylDc6hhjm8yxZMHRyDfLBy7oIXkMHVIi_gBdznwxLax2DQNBWoFemC1gSDGpxprWlABbfGmtrAT8MO2ipl5fTu195DN6OT6-FpOLkYnw0Hk1AlcZqFLMoY47lUuZRFrnScFbiUNMEsZSqPtL9hPCoLzLkqaJaqSOGY51FWasyKlMU9dLDubax5XmjXijk4pSv_OW0WTpA0ppRjb8ij-7_QmVnY2k_nKeKdJQSnnjpcU8oa56wuRWNhLu2bIFh8mhbetFiZ9mz_F6ugXflprYTqv8QSKv32d7UYjkffiXCdANfq15-EtE-C8ZhTcTcdi9Mxj6d0eiXS-AO2p6Fb |
| CitedBy_id | crossref_primary_10_1090_mcom_3839 crossref_primary_10_1016_j_comgeo_2020_101683 |
| Cites_doi | 10.1016/j.comgeo.2015.04.002 10.1002/9780470317013 10.1007/978-3-540-33259-6 10.1137/0717044 10.1016/j.cad.2012.10.043 10.1007/BF02187681 10.1007/s00454-011-9345-9 10.1007/BF02187890 10.1016/j.jsc.2011.08.021 10.1142/8685 10.1142/S0218195906002191 10.1016/B978-044482537-7/50006-1 |
| ContentType | Journal Article |
| Copyright | 2016 The Author(s) Computer Graphics Forum © 2016 The Eurographics Association and John Wiley & Sons Ltd. Published by John Wiley & Sons Ltd. 2016 The Eurographics Association and John Wiley & Sons Ltd. |
| Copyright_xml | – notice: 2016 The Author(s) Computer Graphics Forum © 2016 The Eurographics Association and John Wiley & Sons Ltd. Published by John Wiley & Sons Ltd. – notice: 2016 The Eurographics Association and John Wiley & Sons Ltd. |
| DBID | BSCLL AAYXX CITATION 7SC 8FD JQ2 L7M L~C L~D F28 FR3 |
| DOI | 10.1111/cgf.12979 |
| 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 | CrossRef Computer and Information Systems Abstracts Technology Research Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering |
| EISSN | 1467-8659 |
| EndPage | 247 |
| ExternalDocumentID | 4147803361 10_1111_cgf_12979 CGF12979 ark_67375_WNG_HG73N5NS_8 |
| 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-c4389-629667bacbaadbce39d0fa540686cb2ece3672fd077cd598c2c037b29fe06d863 |
| IEDL.DBID | DRFUL |
| ISICitedReferencesCount | 6 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000383444500023&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 | Sun Nov 09 12:00:13 EST 2025 Fri Jul 25 23:44:57 EDT 2025 Sat Nov 29 03:41:13 EST 2025 Tue Nov 18 21:31:33 EST 2025 Wed Jan 22 16:45:13 EST 2025 Tue Nov 11 03:31:49 EST 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 5 |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c4389-629667bacbaadbce39d0fa540686cb2ece3672fd077cd598c2c037b29fe06d863 |
| Notes | ArticleID:CGF12979 istex:FE3E80C9E7922B52CEDE558E09766C85AE01521A ark:/67375/WNG-HG73N5NS-8 Chee and Huck are supported by NSF Grant #CCF‐1423228. Evanthia is supported by SNSF #20GG21‐134355, #200021E‐154387. SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-1 ObjectType-Feature-2 content type line 23 |
| PQID | 1811464108 |
| PQPubID | 30877 |
| PageCount | 19 |
| ParticipantIDs | proquest_miscellaneous_1835570111 proquest_journals_1811464108 crossref_primary_10_1111_cgf_12979 crossref_citationtrail_10_1111_cgf_12979 wiley_primary_10_1111_cgf_12979_CGF12979 istex_primary_ark_67375_WNG_HG73N5NS_8 |
| PublicationCentury | 2000 |
| PublicationDate | August 2016 |
| PublicationDateYYYYMMDD | 2016-08-01 |
| PublicationDate_xml | – month: 08 year: 2016 text: August 2016 |
| PublicationDecade | 2010 |
| PublicationPlace | Oxford |
| PublicationPlace_xml | – name: Oxford |
| PublicationTitle | Computer graphics forum |
| PublicationTitleAlternate | Computer Graphics Forum |
| PublicationYear | 2016 |
| Publisher | Blackwell Publishing Ltd |
| Publisher_xml | – name: Blackwell Publishing Ltd |
| References | Aurenhammer F., Klein R., Lee D.-T.: Voronoi Diagrams and Delaunay Triangulations. World Scientific, 2013. 1 Lin L., Yap C.: Adaptive isotopic approximation of nonsingular curves: the parameterizability and nonlocal isotopy approach. Discrete and Comp. Geom. 45, 4 (2011), 760-795. 14 Ratschek H., Rokne J.: Computer Methods for the Range of Functions. Horwood Publishing Limited, Chichester, West Sussex, UK, 1984. 5 Munkres J.R.: Elements of Algebraic Topology. The Benjamin/Cummings Publishing Company, Inc, Menlo Park, CA, 1984. 2 Edelsbrunner H., Seidel R.: Voronoi diagrams and arrangements. Discrete and Comp. Geom. 1 (1986), 25-44. 2 Emiris I., Mantzaflaris A., Mourrain B.: Voronoi Diagrams of algebraic distance fields. Computer Aided Design 45, 2 (2013), 511-516. 2, 4, 9 Burr M., Choi S., Galehouse B., Yap C.: Complete subdivision algorithms, II: Isotopic meshing of singular algebraic curves. J. Symbolic Computation 47, 2 (2012), 131-152. Special Issue for ISSAC 2008. 3, 6, 14, 15 Wang C., Chiang Y.-J., Yap C.: On Soft Predicates in Subdivision Motion Planning. Comput. Geometry: Theory and Appl. 48, 8 (Sept. 2015), 589-605. doi: 10.1016/j.comgeo.2015.04.002. 2 Moore R.E., Kioustelidis J.B.: A simple test for accuracy of approximate solutions to nonlinear (or linear) systems. SIAM J. Numer. Anal. 17, 4 (1980), 521-529. 6, 15, 16 Yap C.K.: An O (nlog n) algorithm for the Voronoi diagram for a set of simple curve segments. Discrete and Comp. Geom. 2 (1987), 365-394. 1 Chang E.-C., Choi S.W., Kwon D., Park H., Yap C.: Shortest paths for disc obstacles is computable. Int'l. J. Comput. Geometry and Appl. 16, 5-6 (2006), 567-590. Special Issue of IJCGA on Geometric Constraints. (Eds. X.S. Gao and D. Michelucci). 2, 3 Okabe A., Boots B., Sugihara K., Chiu S.N.: Spatial Tessellations - Concepts and Applications of Voronoi Diagrams, 2nd ed. John Wiley and Sons, 2000. 1 Samet H.: The Design and Analysis of Spatial Data Structures. Addison Wesley, 1990. 2 1980; 17 1986; 1 2015; 48 1987; 2 2012 2000 2013; 7921 2013; 45 2006; 16 2 2006 2014; 8503 1984 2016 2014; 2014 2011; 45 1993 2004 2003 2013 2012; 47 1989 e_1_2_7_5_2 e_1_2_7_4_2 e_1_2_7_3_2 e_1_2_7_2_2 e_1_2_7_9_2 e_1_2_7_8_2 Lien J.‐M. (e_1_2_7_13_2) 2014 e_1_2_7_6_2 e_1_2_7_17_2 e_1_2_7_15_2 e_1_2_7_14_2 e_1_2_7_10_2 Labelle F. (e_1_2_7_12_2) 2003 Ratschek H. (e_1_2_7_21_2) 1984 Klein R. (e_1_2_7_11_2) 1989 Milenkovic V. (e_1_2_7_16_2) 1993 Yap C. (e_1_2_7_25_2) 2012 Bennett H. (e_1_2_7_7_2) 2014 e_1_2_7_24_2 Yap C. (e_1_2_7_26_2) 2013 e_1_2_7_23_2 Munkres J.R. (e_1_2_7_18_2) 1984 Okabe A. (e_1_2_7_19_2) 2000 Plantinga S. (e_1_2_7_20_2) 2004 Samet H. (e_1_2_7_22_2); 2 |
| References_xml | – reference: Samet H.: The Design and Analysis of Spatial Data Structures. Addison Wesley, 1990. 2 – reference: Okabe A., Boots B., Sugihara K., Chiu S.N.: Spatial Tessellations - Concepts and Applications of Voronoi Diagrams, 2nd ed. John Wiley and Sons, 2000. 1 – reference: Ratschek H., Rokne J.: Computer Methods for the Range of Functions. Horwood Publishing Limited, Chichester, West Sussex, UK, 1984. 5 – reference: Moore R.E., Kioustelidis J.B.: A simple test for accuracy of approximate solutions to nonlinear (or linear) systems. SIAM J. Numer. Anal. 17, 4 (1980), 521-529. 6, 15, 16 – reference: Wang C., Chiang Y.-J., Yap C.: On Soft Predicates in Subdivision Motion Planning. Comput. Geometry: Theory and Appl. 48, 8 (Sept. 2015), 589-605. doi: 10.1016/j.comgeo.2015.04.002. 2 – reference: Edelsbrunner H., Seidel R.: Voronoi diagrams and arrangements. Discrete and Comp. Geom. 1 (1986), 25-44. 2 – reference: Lin L., Yap C.: Adaptive isotopic approximation of nonsingular curves: the parameterizability and nonlocal isotopy approach. Discrete and Comp. Geom. 45, 4 (2011), 760-795. 14 – reference: Yap C.K.: An O (nlog n) algorithm for the Voronoi diagram for a set of simple curve segments. Discrete and Comp. Geom. 2 (1987), 365-394. 1 – reference: Munkres J.R.: Elements of Algebraic Topology. The Benjamin/Cummings Publishing Company, Inc, Menlo Park, CA, 1984. 2 – reference: Burr M., Choi S., Galehouse B., Yap C.: Complete subdivision algorithms, II: Isotopic meshing of singular algebraic curves. J. Symbolic Computation 47, 2 (2012), 131-152. Special Issue for ISSAC 2008. 3, 6, 14, 15 – reference: Emiris I., Mantzaflaris A., Mourrain B.: Voronoi Diagrams of algebraic distance fields. Computer Aided Design 45, 2 (2013), 511-516. 2, 4, 9 – reference: Chang E.-C., Choi S.W., Kwon D., Park H., Yap C.: Shortest paths for disc obstacles is computable. Int'l. J. Comput. Geometry and Appl. 16, 5-6 (2006), 567-590. Special Issue of IJCGA on Geometric Constraints. (Eds. X.S. Gao and D. Michelucci). 2, 3 – reference: Aurenhammer F., Klein R., Lee D.-T.: Voronoi Diagrams and Delaunay Triangulations. World Scientific, 2013. 1 – volume: 16 start-page: 567 issue: 5 year: 2006 end-page: 6 590 article-title: Shortest paths for disc obstacles is computable publication-title: Int'l. J. Comput. Geometry and Appl. – volume: 47 start-page: 131 issue: 2 year: 2012 end-page: 152 article-title: Complete subdivision algorithms, II: Isotopic meshing of singular algebraic curves publication-title: J. Symbolic Computation – volume: 1 start-page: 25 year: 1986 end-page: 44 article-title: Voronoi diagrams and arrangements publication-title: Discrete and Comp. Geom. – start-page: 191 year: 2003 end-page: 200 – volume: 7921 start-page: 434 year: 2013 end-page: 444 – year: 1984 – year: 2016 article-title: Complexity analysis of root clustering for a complex polynomial – start-page: 473 year: 1993 end-page: 478 – volume: 2 article-title: The Design and Analysis of Spatial Data Structures. publication-title: Addison Wesley, 1990. – year: 2006 – year: 1989 – year: 2000 – volume: 2014 start-page: 277 year: 2014 end-page: 282 – start-page: 201 year: 2000 end-page: 290 – volume: 17 start-page: 521 issue: 4 year: 1980 end-page: 529 article-title: A simple test for accuracy of approximate solutions to nonlinear (or linear) systems publication-title: SIAM J. Numer. Anal. – volume: 45 start-page: 511 issue: 2 year: 2013 end-page: 516 article-title: Voronoi Diagrams of algebraic distance fields publication-title: Computer Aided Design – volume: 8503 start-page: 38 year: 2014 end-page: 49 – volume: 2 start-page: 365 year: 1987 end-page: 394 article-title: An ( log ) algorithm for the Voronoi diagram for a set of simple curve segments publication-title: Discrete and Comp. Geom. – start-page: 760 end-page: 795 article-title: Adaptive isotopic approximation of nonsingular curves: the parameterizability and nonlocal isotopy approach – volume: 45 start-page: 760 issue: 4 year: 2011 end-page: 795 article-title: Adaptive isotopic approximation of nonsingular curves: the parameterizability and nonlocal isotopy approach publication-title: Discrete and Comp. Geom. – start-page: 245 year: 2004 end-page: 254 – year: 2013 – volume: 48 start-page: 589 issue: 8 year: 2015 end-page: 605 article-title: On Soft Predicates in Subdivision Motion Planning publication-title: Comput. Geometry: Theory and Appl. – start-page: 2 year: 2012 end-page: 16 – ident: e_1_2_7_5_2 – ident: e_1_2_7_23_2 doi: 10.1016/j.comgeo.2015.04.002 – volume-title: Spatial Tessellations — Concepts and Applications of Voronoi Diagrams year: 2000 ident: e_1_2_7_19_2 doi: 10.1002/9780470317013 – ident: e_1_2_7_6_2 doi: 10.1007/978-3-540-33259-6 – ident: e_1_2_7_17_2 doi: 10.1137/0717044 – ident: e_1_2_7_9_2 doi: 10.1016/j.cad.2012.10.043 – ident: e_1_2_7_10_2 doi: 10.1007/BF02187681 – ident: e_1_2_7_15_2 doi: 10.1007/s00454-011-9345-9 – volume-title: Computer Methods for the Range of Functions year: 1984 ident: e_1_2_7_21_2 – ident: e_1_2_7_24_2 doi: 10.1007/BF02187890 – start-page: 38 volume-title: Lect. Notes in C.S year: 2014 ident: e_1_2_7_7_2 – start-page: 277 volume-title: ICMS year: 2014 ident: e_1_2_7_13_2 – start-page: 191 volume-title: Proc. 19th ACM Symp. on Comp. Geom. year: 2003 ident: e_1_2_7_12_2 – start-page: 473 volume-title: Proc. 5th Canadian Conf. on Computational Geom. (CCCG) (1993) year: 1993 ident: e_1_2_7_16_2 – ident: e_1_2_7_4_2 doi: 10.1016/j.jsc.2011.08.021 – ident: e_1_2_7_14_2 doi: 10.1007/s00454-011-9345-9 – volume-title: Elements of Algebraic Topology year: 1984 ident: e_1_2_7_18_2 – ident: e_1_2_7_3_2 doi: 10.1142/8685 – ident: e_1_2_7_8_2 doi: 10.1142/S0218195906002191 – volume: 2 ident: e_1_2_7_22_2 article-title: The Design and Analysis of Spatial Data Structures. publication-title: Addison Wesley, 1990. – start-page: 2 volume-title: 9th Proc. Int'l. Symp. of Voronoi Diagrams in Science and Engineering (ISVD). year: 2012 ident: e_1_2_7_25_2 – start-page: 245 volume-title: Proc. Eurographics Symposium on Geometry Processing year: 2004 ident: e_1_2_7_20_2 – start-page: 434 volume-title: Lect. Notes in C.S year: 2013 ident: e_1_2_7_26_2 – ident: e_1_2_7_2_2 doi: 10.1016/B978-044482537-7/50006-1 – volume-title: Lecture Notes in Computer Science, No. 400 year: 1989 ident: e_1_2_7_11_2 |
| SSID | ssj0004765 |
| Score | 2.2236872 |
| Snippet | Let X = {f1, …, fn} be a set of scalar functions of the form fi : ℝ2 → ℝ which satisfy some natural properties. We describe a subdivision algorithm for... Let X = {f 1 , …, f n } be a set of scalar functions of the form f i : ℝ 2 → ℝ which satisfy some natural properties. We describe a subdivision algorithm for... Let X = {f1, ..., fn} be a set of scalar functions of the form fi : 2 [arrow right] which satisfy some natural properties. We describe a subdivision algorithm... Let X = {f sub(1), ..., f sub(n)} be a set of scalar functions of the form f sub(i) : super(2) arrow right which satisfy some natural properties. We describe a... |
| SourceID | proquest crossref wiley istex |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 229 |
| SubjectTerms | Algorithms Anisotropy Categories and Subject Descriptors (according to ACM CCS) F.2.2 [Analysis of Algorithms and Problem Complexity]: Nonnumerical Algorithms and Problems-Geometrical problems and computations G.1.0 [Numerical Analysis]: General-Interval arithmetic G.1.2 [Numerical Analysis]: Approximation-Approximation of surfaces and contours G.4 [Mathematical Software]: -Algorithm design and analysis I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling-Geometric algorithms Image processing systems Mathematical analysis Mathematical models Minimization Optimization Scalars Studies Subdivisions |
| Title | Planar Minimization Diagrams via Subdivision with Applications to Anisotropic Voronoi Diagrams |
| URI | https://api.istex.fr/ark:/67375/WNG-HG73N5NS-8/fulltext.pdf https://onlinelibrary.wiley.com/doi/abs/10.1111%2Fcgf.12979 https://www.proquest.com/docview/1811464108 https://www.proquest.com/docview/1835570111 |
| Volume | 35 |
| WOSCitedRecordID | wos000383444500023&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/eLvHCXMwpV1Lj9QwDLaWGQ5w4L1iYEEBIcSlqNNHHuI02mVmD1AhYGFPREmaogpoV-3sip-P3RezEkhI3KrGaSPHjp3E_gzwzFjlrVNxUCRLGSSFWAbWiSTw0qjciwSX5b7YhMgyeXqq3u3BqzEXpseHmA7cSDO69ZoU3Nh2R8nd1-IlGiuhrsA8QrlNZzA_er8-efM7LVLwdIT2JtCYAViIAnmmzpfM0Zw4-_OSr7nrsXYmZ33zvwZ7C24MniZb9aJxG_Z8dQeu7-AP3oUvVLLINOxtWZU_hoRMdlQaithq2UVpGK4rlLBFR2qMjmzZaufCm21rtqrKtt429Vnp2CdCQ6jL6Qv34GT9-uPhcTAUXAgcFUEPeISbH2GNs8bk1vlY5WFh0KfjkjsbeXzDRVTkoRAuT5V0kQtjYSNV-JDnksf7MKvqyt8HxnGfkoYF4RXyRBJmlfIhysMylSH2ixbwYuS7dgMaORXF-K7HXQmyTHcsW8DTifSsh-D4E9HzbvImCtN8o5g1kerP2UYfb0ScpdkHLRdwMM6uHtS11ejmoMVIliE2P5maUdHo9sRUvj4nmpjgyvCvOPZurv8-Gn24WXcPD_6d9CFcQ2eM98GFBzDbNuf-EVx1F9uybR4Psv0L4-78bw |
| linkProvider | Wiley-Blackwell |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3da9RAEB9qT1Af_BZPq64i4kskl4_9AF-O1rsTr0G01T65bDYbCbZJyV1L__zO5MsrKAi-hexssuzO7MzOzvwG4LVJlUutCr08mkgvysXES62IPCeNypyIcFtui02IJJFHR-rzFrzvc2FafIjB4UaS0ezXJODkkN6Qcvszf4faSqhrMIqQjZC_R3tfZofL33mRgsc9tjehxnTIQhTJM3S-oo9GNLUXV4zNTZO10TmzO_832rtwu7M12bRljnuw5cr7cGsDgfAB_KCiRaZm-0VZnHQpmWyvMBSztWLnhWG4s1DKFjnVGDlt2XTjyputKzYti1W1rqvTwrJvhIdQFcMXHsLh7MPB7sLrSi54lsqgezzA449IjU2NyVLrQpX5uUGrjktu08DhGy6CPPOFsFmspA2sH4o0ULnzeSZ5-Ai2y6p0j4FxPKnEfk6IhTyShFqlnI8cMYmlj_2CMbztJ17bDo-cymIc6_5cglOmmykbw6uB9LQF4fgT0Ztm9QYKU_-iqDUR6-_JXC_mIkzi5KuWY9jpl1d3ArvSaOigzogmPja_HJpR1Oj-xJSuOiOakADL8K849max_z4avTufNQ9P_p30BdxYHOwv9fJj8ukp3ETTjLehhjuwva7P3DO4bs_Xxap-3jH6JQBKAG4 |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3da9RAEB_qnUh9aP1o6Wmrq4j4kpLLx35AX45ecxVrKGq1T102m00JrcmRuxb_fHfy1SsoCL6F7GyyzO7szOzO_AbgnUqESbTwnSwYcyfI2NhJNAscw5VIDQvsttwUm2BxzM_PxekaHHS5MA0-RH_ghpJR79co4GaeZitSri-zfautmHgAwwCLyAxgOP0SnZ3c5UUyGnbY3oga0yILYSRP3_mePhoia3_dMzZXTdZa50Sb_zfaJ7DR2ppk0iyOp7BmimfweAWB8DlcYNEiVZHPeZH_bFMyyTRXGLO1ILe5InZnwZQtPFQjeGhLJitX3mRZkkmRL8plVc5zTb4jHkKZ91_YgrPo6NvhsdOWXHA0lkF3qGfdH5YonSiVJtr4InUzZa06yqlOPGPfUOZlqcuYTkPBtaddnyWeyIxLU079bRgUZWF2gFDrqYRuhoiFNOCIWiWMa1fEOOSu7eeN4EPHeKlbPHIsi3EtO7_EskzWLBvB25503oBw_InofT17PYWqrjBqjYXyRzyTxzPmx2H8VfIR7HbTK1uBXUhr6FidEYxd2_ymb7aihvcnqjDlDdL4CFhm_2rHXk_230cjD2dR_fDi30lfw6PTaSRPPsafXsK6tcxoE2m4C4NldWP24KG-XeaL6lW7zn8Divr_2g |
| 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=Planar+Minimization+Diagrams+via+Subdivision+with+Applications+to+Anisotropic+Voronoi+Diagrams&rft.jtitle=Computer+graphics+forum&rft.au=Bennett%2C+H.&rft.au=Papadopoulou%2C+E.&rft.au=Yap%2C+C.&rft.date=2016-08-01&rft.pub=Blackwell+Publishing+Ltd&rft.issn=0167-7055&rft.eissn=1467-8659&rft.volume=35&rft.issue=5&rft.spage=229&rft.epage=247&rft_id=info:doi/10.1111%2Fcgf.12979&rft.externalDBID=n%2Fa&rft.externalDocID=ark_67375_WNG_HG73N5NS_8 |
| 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 |