Proximity Queries Between Convex Objects: An Interior Point Approach for Implicit Surfaces
This paper presents a general method for exact distance computation between convex objects represented as intersections of implicit surfaces. Exact distance computation algorithms are particularly important for applications involving objects that make intermittent contact, such as in dynamic simulat...
Saved in:
| Published in: | IEEE transactions on robotics Vol. 24; no. 1; pp. 211 - 220 |
|---|---|
| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
New York, NY
IEEE
01.02.2008
Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Subjects: | |
| ISSN: | 1552-3098, 1941-0468 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | This paper presents a general method for exact distance computation between convex objects represented as intersections of implicit surfaces. Exact distance computation algorithms are particularly important for applications involving objects that make intermittent contact, such as in dynamic simulations and in haptic interactions. They can also be used in the narrow phase of hierarchical collision detection. In contrast to geometric approaches developed for polyhedral objects, we formulate the distance computation problem as a convex optimization problem. We use an interior point method to solve the optimization problem and demonstrate that, for general convex objects represented as implicit surfaces, interior point approaches are globally convergent, and fast in practice. Further, they provide polynomial-time guarantees for implicit surface objects when the implicit surfaces have self-concordant barrier functions. We use a primal-dual interior point algorithm that solves the Karush-Kuhn-Tucker (KKT) conditions obtained from the convex programming formulation. For the case of polyhedra and quadrics, we establish a theoretical time complexity of O(n 1.5 ), where n is the number of constraints. We present implementation results for example implicit surface objects, including polyhedra, quadrics, and generalizations of quadrics such as superquadrics and hyperquadrics, as well as intersections of these surfaces. We demonstrate that in practice, the algorithm takes time linear in the number of constraints, and that distance computation rates of about 1 kHz can be achieved. We also extend the approach to proximity queries between deforming convex objects. Finally, we show that continuous collision detection for linearly translating objects can be performed by solving two related convex optimization problems. For polyhedra and quadrics, we establish that the computational complexity of this problem is also O(n 1.5 ). |
|---|---|
| AbstractList | This paper presents a general method for exact distance computation between convex objects represented as intersections of implicit surfaces. Exact distance computation algorithms are particularly important for applications involving objects that make intermittent contact, such as in dynamic simulations and in haptic interactions. They can also be used in the narrow phase of hierarchical collision detection. In contrast to geometric approaches developed for polyhedral objects, we formulate the distance computation problem as a convex optimization problem. We use an interior point method to solve the optimization problem and demonstrate that, for general convex objects represented as implicit surfaces, interior point approaches are globally convergent, and fast in practice. Further, they provide polynomial-time guarantees for implicit surface objects when the implicit surfaces have self-concordant barrier functions. We use a primal-dual interior point algorithm that solves the Karush-Kuhn-Tucker (KKT) conditions obtained from the convex programming formulation. For the case of polyhedra and quadrics, we establish a theoretical time complexity of O(n super(1.5)), where n is the number of constraints. We present implementation results for example implicit surface objects, including polyhedra, quadrics, and generalizations of quadrics such as superquadrics and hyperquadrics, as well as intersections of these surfaces. We demonstrate that in practice, the algorithm takes time linear in the number of constraints, and that distance computation rates of about 1 kHz can be achieved. We also extend the approach to proximity queries between deforming convex objects. Finally, we show that continuous collision detection for linearly translating objects can be performed by solving two related convex optimization problems. For polyhedra and quadrics, we establish that the computational complexity of this problem is also O(n super(1.5)). This paper presents a general method for exact distance computation between convex objects represented as intersections of implicit surfaces. Exact distance computation algorithms are particularly important for applications involving [abstract truncated by publisher]. This paper presents a general method for exact distance computation between convex objects represented as intersections of implicit surfaces. Exact distance computation algorithms are particularly important for applications involving objects that make intermittent contact, such as in dynamic simulations and in haptic interactions. They can also be used in the narrow phase of hierarchical collision detection. In contrast to geometric approaches developed for polyhedral objects, we formulate the distance computation problem as a convex optimization problem. We use an interior point method to solve the optimization problem and demonstrate that, for general convex objects represented as implicit surfaces, interior point approaches are globally convergent, and fast in practice. Further, they provide polynomial-time guarantees for implicit surface objects when the implicit surfaces have self-concordant barrier functions. We use a primal-dual interior point algorithm that solves the Karush-Kuhn-Tucker (KKT) conditions obtained from the convex programming formulation. For the case of polyhedra and quadrics, we establish a theoretical time complexity of O(n 1.5 ), where n is the number of constraints. We present implementation results for example implicit surface objects, including polyhedra, quadrics, and generalizations of quadrics such as superquadrics and hyperquadrics, as well as intersections of these surfaces. We demonstrate that in practice, the algorithm takes time linear in the number of constraints, and that distance computation rates of about 1 kHz can be achieved. We also extend the approach to proximity queries between deforming convex objects. Finally, we show that continuous collision detection for linearly translating objects can be performed by solving two related convex optimization problems. For polyhedra and quadrics, we establish that the computational complexity of this problem is also O(n 1.5 ). This paper presents a general method for exact distance computation between convex objects represented as intersections of implicit surfaces. Exact distance computation algorithms are particularly important for applications involving objects that make intermittent contact, such as in dynamic simulations and in haptic interactions. They can also be used in the narrow phase of hierarchical collision detection. In contrast to geometric approaches developed for polyhedral objects, we formulate the distance computation problem as a convex optimization problem. We use an interior point method to solve the optimization problem and demonstrate that, for general convex objects represented as implicit surfaces, interior point approaches are globally convergent, and fast in practice. Further, they provide polynomial-time guarantees for implicit surface objects when the implicit surfaces have self-concordant barrier functions. We use a primal-dual interior point algorithm that solves the Karush-Kuhn-Tucker (KKT) conditions obtained from the convex programming formulation. For the case of polyhedra and quadrics, we establish a theoretical time complexity of $O(n^{1.5})$, where $n$ is the number of constraints. We present implementation results for example implicit surface objects, including polyhedra, quadrics, and generalizations of quadrics such as superquadrics and hyperquadrics, as well as intersections of these surfaces. We demonstrate that in practice, the algorithm takes time linear in the number of constraints, and that distance computation rates of about 1 kHz can be achieved. We also extend the approach to proximity queries between deforming convex objects. Finally, we show that continuous collision detection for linearly translating objects can be performed by solving two related convex optimization problems. For polyhedra and quadrics, we establish that the - computational complexity of this problem is also $O(n^{1.5})$. [PUBLICATION ABSTRACT] |
| Author | Chakraborty, N. Mitchell, J.E. Jufeng Peng Akella, S. |
| Author_xml | – sequence: 1 givenname: N. surname: Chakraborty fullname: Chakraborty, N. organization: Dept. of Comput. Sci., Rensselaer Polytech. Inst., Troy, NY – sequence: 2 surname: Jufeng Peng fullname: Jufeng Peng – sequence: 3 givenname: S. surname: Akella fullname: Akella, S. – sequence: 4 givenname: J.E. surname: Mitchell fullname: Mitchell, J.E. |
| BackLink | http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=20158232$$DView record in Pascal Francis |
| BookMark | eNqFkUtvEzEURi1UJPpas2BjIQGrSX39yphdiIBGqpQWyobNyOPYwtHEDrYH2n-PR6m66KKsfGWd7z50TtBRiMEi9BrIDICoi9tv6xklZD5TwFsBL9AxKA4N4bI9qrUQtGFEta_QSc5bQihXhB2jn9cp3vmdL_f4ZrTJ24w_2fLX2oCXMfyxd3jdb60p-SNeBLwKpTIx4evoQ8GL_T5FbX5hV79Wu_3gjS_4-5icNjafoZdOD9meP7yn6MeXz7fLy-Zq_XW1XFw1hgMrDQXCpJpL2ivNNCjNXa84E0SIDWhnwDKQ1CkgG9VrRuXGSSeZEaynm95Idoo-HPrWZX6PNpdu57Oxw6CDjWPu6p2SiZbCf8m2Vawlc5jI98-SjHMARabhb5-A2zimUO_tKAEJSrEJevcA6Wz04JIOxudun_xOp_sJrOsxWrmLA2dSzDlZ94gA6SbJXZXcTZK7g-SaEE8S1YAuPoaStB-eyb055Ly19nEK50LOOWH_AEoFs5Y |
| CODEN | ITREAE |
| CitedBy_id | crossref_primary_10_1016_j_cad_2021_103133 crossref_primary_10_1007_s00500_013_1005_y crossref_primary_10_1109_TGCN_2023_3269283 crossref_primary_10_1017_S0263574719001139 crossref_primary_10_1016_j_cma_2012_04_006 crossref_primary_10_1108_AA_03_2015_018 crossref_primary_10_1109_TRO_2024_3502214 crossref_primary_10_1007_s40571_019_00232_5 crossref_primary_10_1016_j_matcom_2011_11_005 crossref_primary_10_1109_LRA_2022_3190629 crossref_primary_10_1109_TRO_2012_2226382 crossref_primary_10_1016_j_trgeo_2024_101377 crossref_primary_10_1177_0278364920983353 crossref_primary_10_1007_s00607_011_0161_0 crossref_primary_10_1016_j_mechmachtheory_2017_04_008 crossref_primary_10_1016_j_mechmachtheory_2010_02_002 crossref_primary_10_1016_j_powtec_2018_08_026 crossref_primary_10_1109_LRA_2017_2668466 crossref_primary_10_1177_0278364913501210 crossref_primary_10_2478_v10180_010_0009_8 crossref_primary_10_1016_j_cad_2019_102777 crossref_primary_10_1016_j_compgeo_2016_12_034 crossref_primary_10_1016_j_apt_2020_06_040 |
| Cites_doi | 10.1109/MCG.1981.1673799 10.1007/s10107-004-0559-y 10.1016/S0097-8493(00)00130-8 10.1023/A:1008677427361 10.1109/56.2083 10.1017/CBO9780511804441 10.1002/(SICI)1097-0207(19960815)39:15<2673::AID-NME972>3.0.CO;2-I 10.1109/ROBOT.1992.220062 10.1137/S1052623401396510 10.1145/285857.285860 10.1137/S1052623499350013 10.1111/1467-8659.t01-1-00587 10.1109/TRO.2004.840906 10.1109/2945.582343 10.1007/0-387-30065-1_4 10.1109/ROBOT.1997.614295 10.1109/ROBOT.1994.351059 10.1080/10867651.1999.10487502 10.1109/70.88117 10.1109/70.650170 10.1109/MCG.2004.59 10.1109/99.714603 10.1007/b98874 10.1142/S0218195997000089 10.1109/70.56661 10.1016/S0734-189X(88)80005-7 10.1109/ROBOT.1991.131723 10.1109/TPAMI.1986.4767773 10.1016/0196-6774(85)90007-0 10.1109/ROBOT.2000.844070 10.1115/1.1884133 10.1109/ROBOT.2000.845311 10.1177/027836498900800304 10.1023/B:JOTA.0000042522.65261.51 10.1145/166117.166158 10.1109/ROBOT.2006.1641985 10.1145/142920.134027 10.1145/97880.97881 |
| ContentType | Journal Article |
| Copyright | 2008 INIST-CNRS Copyright Institute of Electrical and Electronics Engineers, Inc. (IEEE) Feb 2008 |
| Copyright_xml | – notice: 2008 INIST-CNRS – notice: Copyright Institute of Electrical and Electronics Engineers, Inc. (IEEE) Feb 2008 |
| DBID | 97E RIA RIE AAYXX CITATION IQODW 7SC 7SP 7TB 8FD FR3 JQ2 L7M L~C L~D F28 |
| DOI | 10.1109/TRO.2007.914851 |
| DatabaseName | IEEE Xplore (IEEE) IEEE All-Society Periodicals Package (ASPP) 1998–Present IEEE Electronic Library (IEL) CrossRef Pascal-Francis Computer and Information Systems Abstracts Electronics & Communications Abstracts Mechanical & Transportation Engineering Abstracts Technology Research Database Engineering 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 |
| DatabaseTitle | CrossRef Technology Research Database Computer and Information Systems Abstracts – Academic Mechanical & Transportation Engineering Abstracts Electronics & Communications Abstracts ProQuest Computer Science Collection Computer and Information Systems Abstracts Engineering Research Database Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Professional ANTE: Abstracts in New Technology & Engineering |
| DatabaseTitleList | Technology Research Database Technology Research Database Technology Research Database Technology Research Database |
| Database_xml | – sequence: 1 dbid: RIE name: IEEE Electronic Library (IEL) url: https://ieeexplore.ieee.org/ sourceTypes: Publisher |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering Applied Sciences |
| EISSN | 1941-0468 |
| EndPage | 220 |
| ExternalDocumentID | 1437049961 20158232 10_1109_TRO_2007_914851 4456740 |
| Genre | orig-research Feature |
| GroupedDBID | .DC 0R~ 29I 4.4 5GY 5VS 6IK 97E AAJGR AARMG AASAJ AAWTH ABAZT ABQJQ ABVLG ACGFO ACIWK AENEX AETIX AGQYO AGSQL AHBIQ AIBXA AKJIK AKQYR ALMA_UNASSIGNED_HOLDINGS ATWAV BEFXN BFFAM BGNUA BKEBE BPEOZ CS3 DU5 EBS EJD F5P HZ~ H~9 IFIPE IPLJI JAVBF LAI M43 MS~ O9- OCL P2P PQQKQ RIA RIE RNS VJK AAYXX CITATION IQODW RIG 7SC 7SP 7TB 8FD FR3 JQ2 L7M L~C L~D F28 |
| ID | FETCH-LOGICAL-c413t-210369762b9a3a19a4fb9435055d1afc1e3162f910d9ba326df6f63c53b2dbc63 |
| IEDL.DBID | RIE |
| ISICitedReferencesCount | 35 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000253789900022&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 1552-3098 |
| IngestDate | Thu Oct 02 11:09:09 EDT 2025 Wed Oct 01 14:53:33 EDT 2025 Sat Sep 27 16:56:12 EDT 2025 Sun Nov 09 07:24:19 EST 2025 Mon Jul 21 09:11:59 EDT 2025 Tue Nov 18 21:42:11 EST 2025 Sat Nov 29 06:22:26 EST 2025 Tue Aug 26 16:47:37 EDT 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 1 |
| Keywords | Intersection Quadric Database query Barrier function Linear time Convex programming Geometrical model Superquadrics User interface Implicit theory Kuhn Tucker condition Dynamic model Mathematical programming Proximity Interior point method Computational complexity Intermittency Polynomial time Polyhedron Phase detector Karush Kuhn Tucker method Primal dual method Collision detection Time complexity Collision avoidance |
| Language | English |
| License | https://ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html CC BY 4.0 |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c413t-210369762b9a3a19a4fb9435055d1afc1e3162f910d9ba326df6f63c53b2dbc63 |
| Notes | SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-2 content type line 23 |
| PQID | 201619936 |
| PQPubID | 23500 |
| PageCount | 10 |
| ParticipantIDs | proquest_miscellaneous_889380711 proquest_journals_201619936 crossref_primary_10_1109_TRO_2007_914851 crossref_citationtrail_10_1109_TRO_2007_914851 ieee_primary_4456740 proquest_miscellaneous_34411906 proquest_miscellaneous_903635821 pascalfrancis_primary_20158232 |
| PublicationCentury | 2000 |
| PublicationDate | 2008-02-01 |
| PublicationDateYYYYMMDD | 2008-02-01 |
| PublicationDate_xml | – month: 02 year: 2008 text: 2008-02-01 day: 01 |
| PublicationDecade | 2000 |
| PublicationPlace | New York, NY |
| PublicationPlace_xml | – name: New York, NY – name: New York |
| PublicationTitle | IEEE transactions on robotics |
| PublicationTitleAbbrev | TRO |
| PublicationYear | 2008 |
| Publisher | IEEE Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Publisher_xml | – name: IEEE – name: Institute of Electrical and Electronics Engineers – name: The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| References | sohn (ref39) 2002 ref35 ref13 ref12 ref37 ref15 ref36 ref31 ref30 ref33 ref11 ref10 lennerz (ref25) 0 ref2 mirtich (ref32) 1995 ref1 ref17 ref38 ref16 ref19 ref18 jimenez (ref23) 2001; 25 peng (ref34) 2005 ref24 lin (ref29) 2004 ref45 ref48 ref26 ref47 ref20 bazaraa (ref3) 1993 ref41 ref22 ref44 ref21 van den bergen (ref42) 2004 copolla (ref14) 1999; 102 waltz (ref46) 2006 ref28 ref27 ref8 ref7 ref9 ref4 ref6 ref5 ref40 bergen (ref43) 2004 |
| References_xml | – year: 1993 ident: ref3 publication-title: Nonlinear Programming Theory and Algorithms – ident: ref2 doi: 10.1109/MCG.1981.1673799 – ident: ref45 doi: 10.1007/s10107-004-0559-y – volume: 25 start-page: 269 year: 2001 ident: ref23 article-title: 3-d collision detection: a survey publication-title: Comput Graph doi: 10.1016/S0097-8493(00)00130-8 – ident: ref44 doi: 10.1023/A:1008677427361 – ident: ref19 doi: 10.1109/56.2083 – ident: ref5 doi: 10.1017/CBO9780511804441 – volume: 102 start-page: 1013 year: 1999 ident: ref14 article-title: determination of close approaches based on ellipsoidal threat volumes – ident: ref40 doi: 10.1002/(SICI)1097-0207(19960815)39:15<2673::AID-NME972>3.0.CO;2-I – ident: ref48 doi: 10.1109/ROBOT.1992.220062 – year: 2004 ident: ref42 publication-title: Collision Detection in Interactive 3-D Environments – ident: ref26 doi: 10.1137/S1052623401396510 – ident: ref31 doi: 10.1145/285857.285860 – ident: ref20 doi: 10.1137/S1052623499350013 – year: 2005 ident: ref34 publication-title: Multiple robot coordination A mathematical programming approach – ident: ref36 doi: 10.1111/1467-8659.t01-1-00587 – ident: ref13 doi: 10.1109/TRO.2004.840906 – ident: ref10 doi: 10.1109/2945.582343 – ident: ref7 doi: 10.1007/0-387-30065-1_4 – ident: ref47 doi: 10.1109/ROBOT.1997.614295 – ident: ref35 doi: 10.1109/ROBOT.1994.351059 – ident: ref41 doi: 10.1080/10867651.1999.10487502 – ident: ref18 doi: 10.1109/70.88117 – ident: ref9 doi: 10.1109/70.650170 – ident: ref30 doi: 10.1109/MCG.2004.59 – ident: ref15 doi: 10.1109/99.714603 – ident: ref33 doi: 10.1007/b98874 – ident: ref27 doi: 10.1142/S0218195997000089 – ident: ref8 doi: 10.1109/70.56661 – ident: ref22 doi: 10.1016/S0734-189X(88)80005-7 – ident: ref28 doi: 10.1109/ROBOT.1991.131723 – ident: ref11 doi: 10.1109/TPAMI.1986.4767773 – start-page: 60 year: 0 ident: ref25 article-title: efficient distance computation for quadratic curves and surfaces – ident: ref16 doi: 10.1016/0196-6774(85)90007-0 – start-page: 236 year: 2002 ident: ref39 article-title: computing the distance between two surfaces via line geometry – year: 2006 ident: ref46 publication-title: Knitro 5 0 User's Manual – ident: ref6 doi: 10.1109/ROBOT.2000.844070 – ident: ref37 doi: 10.1115/1.1884133 – ident: ref24 doi: 10.1109/ROBOT.2000.845311 – year: 2004 ident: ref43 publication-title: Ray casting against general convex objects with application to continuous collision detection – ident: ref4 doi: 10.1177/027836498900800304 – year: 1995 ident: ref32 publication-title: Algorithmic Foundations of Robotics – ident: ref21 doi: 10.1023/B:JOTA.0000042522.65261.51 – ident: ref38 doi: 10.1145/166117.166158 – ident: ref12 doi: 10.1109/ROBOT.2006.1641985 – start-page: 787 year: 2004 ident: ref29 publication-title: Handbook of Discrete and Computational Geometry – ident: ref17 doi: 10.1145/142920.134027 – ident: ref1 doi: 10.1145/97880.97881 |
| SSID | ssj0024903 |
| Score | 2.0925653 |
| Snippet | This paper presents a general method for exact distance computation between convex objects represented as intersections of implicit surfaces. Exact distance... |
| SourceID | proquest pascalfrancis crossref ieee |
| SourceType | Aggregation Database Index Database Enrichment Source Publisher |
| StartPage | 211 |
| SubjectTerms | Algorithms Application software Applied sciences Closest points collision detection Computation Computational complexity Computational modeling Computer science; control theory; systems Constraint theory Control theory. Systems Exact sciences and technology Haptic interfaces implicit surfaces Information systems. Data bases interior point algorithms Intersections Mathematical programming Memory organisation. Data processing Object detection Optimization Optimization algorithms Optimization methods Phase detection Polyhedra Polyhedrons Polynomials Problem solving Programming profession Proximity proximity query Queries Robotics Software |
| Title | Proximity Queries Between Convex Objects: An Interior Point Approach for Implicit Surfaces |
| URI | https://ieeexplore.ieee.org/document/4456740 https://www.proquest.com/docview/201619936 https://www.proquest.com/docview/34411906 https://www.proquest.com/docview/889380711 https://www.proquest.com/docview/903635821 |
| Volume | 24 |
| WOSCitedRecordID | wos000253789900022&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: PRVIEE databaseName: IEEE Electronic Library (IEL) customDbUrl: eissn: 1941-0468 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0024903 issn: 1552-3098 databaseCode: RIE dateStart: 20040101 isFulltext: true titleUrlDefault: https://ieeexplore.ieee.org/ providerName: IEEE |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV3LbtUwEB2VigUseBVEKBQvWLAgbZyHHbO7VFSwaS9QpIpNZDu2dKUqQXmg8vfMOGmggrtgF8kTyfLYnmP7zBmAV8YImyrN8ZDjVZz7Oo-N0TYWiTGF8hI3yzoUm5Cnp-XFhVrvwJslF8Y5F8hn7pA-w1t-3dqRrsqOcoz2MscD-i0pxZSr9VtXT4UqyKQoFmeJKmcZH56oo_PPZ5NWoULsX_AbESiUVCFCpO5xTPxUzOKvfTkEm5P7_9fNB3BvBpVsNc2Ch7Djmkdw9w-pwT34tu7aK0pm-sk-jSRu3LN3E0WLHRPx_IqdGbqS6d-yVcPCPeGm7di63TQDW83C4wwRLvsYOOibgX0ZO0-Ersfw9eT9-fGHeK6rEFsMWUOMp7xMIAxJjdKZ5krn3iiETUlR1Fx7y13GBbqOJ7UyGvFd7YUXmS0yk9bGiuwJ7DZt454C09ykQhKMzF3OS6cxuFlVlJqntZZWRnB4PdaVnUXHqfbFZRUOH4mq0DlUClNWk3MieL388H3S29huukdjv5jNwx7BwQ1nLu0IdYoSAWQE-9fereYF21OjIC6jiODl0oorjZ5PdOPasa8yRI4In9CCbbEoEfyViNn4dhNFD-eUnPzs373fhzsTI4UIM89hd-hG9wJu2x_Dpu8OwpT_BQbj_u4 |
| linkProvider | IEEE |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1Nb9QwEB1VBQk4UKBUhNLWBw4cSBvnw4m5bSuqVpTtAotUcYlsx5FWQgnKByr_nhknDa1gD9wieSJZHtvzbL95A_Baa2FCqTgeckrpx2UR-1or44tA60SWKW6WhSs2kc7n2dWVXGzA2ykXxlrryGf2kD7dW35Rm56uyo5ijPZpjAf0e0kch8GQrfVHWU-6OsikKeZHgcxGIR8eyKPl58tBrVAi-k_4nRjkiqoQJVK1OCrlUM7ir53ZhZvTrf_r6BN4PMJKNhvmwVPYsNUzeHRLbHAbvi2a-prSmX6xTz3JG7fseCBpsROinl-zS02XMu07NquYuylc1Q1b1KuqY7NRepwhxmXnjoW-6tiXvimJ0vUcvp6-X56c-WNlBd9g0Op8POdFAoFIqKWKFJcqLrVE4BQkScFVabiNuEDn8aCQWiHCK0pRisgkkQ4LbUS0A5tVXdkXwBTXoUgJSMY25plVGN6MTDLFw0KlJvXg8GasczPKjlP1i--5O34EMkfnUDHMNB-c48Gb6Ycfg-LGetNtGvvJbBx2D_bvOHNqR7CTZAghPdi98W4-LtmWGgWxGYUHB1MrrjV6QFGVrfs2jxA7IoBCC7bGIkP4lyFq4-tNJD2dU3ryy3_3_gAenC0_XuQX5_MPu_Bw4KcQfeYVbHZNb_fgvvnZrdpm303_32hhAkQ |
| 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=Proximity+Queries+Between+Convex+Objects%3A+An+Interior+Point+Approach+for+Implicit+Surfaces&rft.jtitle=IEEE+transactions+on+robotics&rft.au=Chakraborty%2C+Nilanjan&rft.au=Peng%2C+Jufeng&rft.au=Akella%2C+Srinivas&rft.au=Mitchell%2C+John+E.&rft.date=2008-02-01&rft.issn=1552-3098&rft.volume=24&rft.issue=1&rft.spage=211&rft.epage=220&rft_id=info:doi/10.1109%2FTRO.2007.914851&rft.externalDBID=n%2Fa&rft.externalDocID=10_1109_TRO_2007_914851 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1552-3098&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1552-3098&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1552-3098&client=summon |