Subdivision scheme tuning around extraordinary vertices
In this paper we extend the standard method to derive and optimize subdivision rules in the vicinity of extraordinary vertices (EV). Starting from a given set of rules for regular control meshes, we tune the extraordinary rules (ER) such that the necessary conditions for C 1 continuity are satisfied...
Saved in:
| Published in: | Computer aided geometric design Vol. 21; no. 6; pp. 561 - 583 |
|---|---|
| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Elsevier B.V
01-07-2004
Elsevier |
| Subjects: | |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | In this paper we extend the standard method to derive and optimize subdivision rules in the vicinity of extraordinary vertices (EV). Starting from a given set of rules for regular control meshes, we tune the extraordinary rules (ER) such that the necessary conditions for
C
1 continuity are satisfied along with as many necessary
C
2 conditions as possible. As usually done, our approach sets up the general configuration around an EV by exploiting rotational symmetry and reformulating the subdivision rules in terms of the subdivision matrix' eigencomponents. The degrees of freedom are then successively eliminated by imposing new constraints which allows us, e.g., to improve the curvature behavior around EVs. The method is flexible enough to simultaneously optimize several subdivision rules, i.e., not only the one for the EV itself but also the rules for its direct neighbors. Moreover, it allows us to prescribe the stencils for the ERs and naturally blends them with the regular rules that are applied away from the EV. All the constraints are combined in an optimization scheme that searches in the space of feasible subdivision schemes for a candidate which satisfies some necessary conditions exactly and other conditions approximately. The relative weighting of the constraints allows us to tune the properties of the subdivision scheme according to application specific requirements. We demonstrate our method by tuning the ERs for the well-known Loop scheme and by deriving ERs for a
3
-type scheme based on a 6-direction Box-spline. |
|---|---|
| AbstractList | In this paper we extend the standard method to derive and optimize subdivision rules in the vicinity of extraordinary vertices (EV). Starting from a given set of rules for regular control meshes, we tune the extraordinary rules (ER) such that the necessary conditions for
C
1 continuity are satisfied along with as many necessary
C
2 conditions as possible. As usually done, our approach sets up the general configuration around an EV by exploiting rotational symmetry and reformulating the subdivision rules in terms of the subdivision matrix' eigencomponents. The degrees of freedom are then successively eliminated by imposing new constraints which allows us, e.g., to improve the curvature behavior around EVs. The method is flexible enough to simultaneously optimize several subdivision rules, i.e., not only the one for the EV itself but also the rules for its direct neighbors. Moreover, it allows us to prescribe the stencils for the ERs and naturally blends them with the regular rules that are applied away from the EV. All the constraints are combined in an optimization scheme that searches in the space of feasible subdivision schemes for a candidate which satisfies some necessary conditions exactly and other conditions approximately. The relative weighting of the constraints allows us to tune the properties of the subdivision scheme according to application specific requirements. We demonstrate our method by tuning the ERs for the well-known Loop scheme and by deriving ERs for a
3
-type scheme based on a 6-direction Box-spline. In this paper we extend the standard method to derive and optimize subdivision rules in the vicinity of extraordinary vertices (EV). Starting from a given set of rules for regular control meshes, we tune the extraordinary rules (ER) such that the necessary conditions for C 1 continuity are satisfied along with as many necessary C 2 conditions as possible. As usually done, our approach sets up the general configuration around an EV by exploiting rotational symmetry and reformulating the subdivision rules in terms of the subdivision matrix' eigencomponents. The degrees of freedom are then successively eliminated by imposing new constraints which allows us, e.g., to improve the curvature behavior around EVs. The method is flexible enough to simultaneously optimize several subdivision rules, i.e. not only the one for the EV itself but also the rules for its direct neighbors. Moreover it allows us to prescribe the stencils for the ERs and naturally blends them with the regular rules that are applied away from the EV. All the constraints are combined in an optimization scheme that searches in the space of feasible subdivision schemes for a candidate which satisfies some necessary conditions exactly and other conditions approximately. The relative weighting of the constraints allows us to tune the properties of the subdivision scheme according to application specific requirements. We demonstrate our method by tuning the ERs for the well-known Loop scheme and by deriving ERs for a √ 3-type scheme based on a 6-direction Box-spline. |
| Author | Kobbelt, Leif Barthe, Loïc |
| Author_xml | – sequence: 1 givenname: Loïc surname: Barthe fullname: Barthe, Loïc email: lbarthe@irit.fr – sequence: 2 givenname: Leif surname: Kobbelt fullname: Kobbelt, Leif email: kobbelt@cs.rwth-aachen.de |
| BackLink | https://hal.science/hal-01538452$$DView record in HAL |
| BookMark | eNp9kEtLAzEUhYNUsK3-AVezdTFjbtLJA9yUolYouFDXIU3utCltRpJp0X_vDBWXwoELl_Pdx5mQUWwjEnILtAIK4n5XObvxFaN0Vg2i_IKMQUldMs7ZiIx7kywV1-KKTHLeUUoZaDEm8u249uEUcmhjkd0WD1h0xxjiprCpPUZf4FeXbJt8iDZ9FydMXXCYr8llY_cZb37rlHw8Pb4vluXq9fllMV-VjkvRlcAa16-urZAaOPdeAF37Bhq59pZaJaTwwnldC1SomGQSpEKNoBVY6TSfkrvz3K3dm88UDv0RprXBLOcrM_Qo1FzNanaC3svOXpfanBM2fwBQM8RkdmaIyQwxmUGU99DDGcL-i1PAZLILGB36kNB1xrfhP_wHk5FxxQ |
| CitedBy_id | crossref_primary_10_1016_j_cad_2023_103544 crossref_primary_10_1111_j_1467_8659_2010_01788_x crossref_primary_10_1145_1531326_1531352 crossref_primary_10_1016_j_cag_2019_05_013 crossref_primary_10_1016_j_cagd_2007_09_001 crossref_primary_10_1111_j_1467_8659_2011_02083_x crossref_primary_10_1016_j_cagd_2018_12_005 crossref_primary_10_1016_j_mod_2017_02_001 crossref_primary_10_1111_cgf_13582 crossref_primary_10_1145_3618400 crossref_primary_10_1145_1141911_1141990 crossref_primary_10_1145_3131778 crossref_primary_10_1016_j_cagd_2005_06_009 crossref_primary_10_1007_s00138_017_0886_7 crossref_primary_10_1016_j_cagd_2007_08_003 crossref_primary_10_1111_cgf_13822 crossref_primary_10_1016_j_cad_2018_04_020 crossref_primary_10_1111_j_1467_8659_2006_00945_x crossref_primary_10_1016_j_cagd_2007_06_001 crossref_primary_10_1111_j_1467_8659_2005_00824_x crossref_primary_10_1016_j_cad_2020_102871 crossref_primary_10_1016_j_cagd_2007_03_009 |
| Cites_doi | 10.1137/S0036142996304346 10.1145/42458.42459 10.1016/S0167-8396(01)00041-3 10.1016/0167-8396(94)00007-F 10.1023/A:1018945708536 10.1007/s003710100148 10.1016/S0167-8396(01)00038-3 10.1016/S0167-8396(01)00039-5 10.1007/s10107-002-0295-0 10.1137/S003614299834263X 10.1016/S0167-8396(01)00040-1 10.1145/263834.263851 10.1016/0010-4485(78)90111-2 10.1016/0010-4485(78)90110-0 |
| ContentType | Journal Article |
| Copyright | 2004 Elsevier B.V. Distributed under a Creative Commons Attribution 4.0 International License |
| Copyright_xml | – notice: 2004 Elsevier B.V. – notice: Distributed under a Creative Commons Attribution 4.0 International License |
| DBID | AAYXX CITATION 1XC VOOES |
| DOI | 10.1016/j.cagd.2004.04.003 |
| DatabaseName | CrossRef Hyper Article en Ligne (HAL) Hyper Article en Ligne (HAL) (Open Access) |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering Mathematics Computer Science |
| EISSN | 1879-2332 |
| EndPage | 583 |
| ExternalDocumentID | oai_HAL_hal_01538452v1 10_1016_j_cagd_2004_04_003 S0167839604000603 |
| GroupedDBID | --K --M -~X .DC .~1 0R~ 1B1 1RT 1~. 1~5 29F 4.4 457 4G. 5GY 5VS 6OB 6TJ 7-5 71M 8P~ 9JN AACTN AAEDT AAEDW AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AAXUO AAYFN ABAOU ABBOA ABFNM ABFSI ABJNI ABMAC ABTAH ABXDB ABYKQ ACAZW ACDAQ ACGFS ACNNM ACRLP ACZNC ADBBV ADEZE ADGUI ADJOM ADMUD AEBSH AEKER AENEX AFFNX AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AHZHX AIALX AIEXJ AIGVJ AIKHN AITUG AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ AOUOD ARUGR ASPBG AVWKF AXJTR AZFZN BKOJK BLXMC CS3 DU5 E.L EBS EFJIC EFLBG EJD EO8 EO9 EP2 EP3 F5P FDB FEDTE FGOYB FIRID FNPLU FYGXN G-2 G-Q G8K GBLVA GBOLZ HLZ HMJ HVGLF HZ~ IHE J1W K-O KOM LG9 M26 M41 MHUIS MO0 N9A O-L O9- OAUVE OZT P-8 P-9 P2P PC. Q38 R2- RIG RNS ROL RPZ SBC SDF SDG SDP SES SEW SME SPC SPCBC SSV SSW SSZ T5K TN5 UHS WUQ XPP ZMT ZY4 ~G- AAXKI AAYXX ABDPE AFJKZ AKRWK CITATION 1XC VOOES |
| ID | FETCH-LOGICAL-c376t-12fc0165a679133dd610bdf1f7bda0a8676d6cd956e8e82727178e9e1981a7c93 |
| ISSN | 0167-8396 |
| IngestDate | Tue Oct 15 15:52:46 EDT 2024 Fri Nov 22 00:15:04 EST 2024 Fri Feb 23 02:29:27 EST 2024 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 6 |
| Keywords | Extraordinary vertices Meshes Artifacts Subdivision surfaces |
| Language | English |
| License | Distributed under a Creative Commons Attribution 4.0 International License: http://creativecommons.org/licenses/by/4.0 |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c376t-12fc0165a679133dd610bdf1f7bda0a8676d6cd956e8e82727178e9e1981a7c93 |
| ORCID | 0000-0001-9908-3640 |
| OpenAccessLink | https://hal.science/hal-01538452 |
| PageCount | 23 |
| ParticipantIDs | hal_primary_oai_HAL_hal_01538452v1 crossref_primary_10_1016_j_cagd_2004_04_003 elsevier_sciencedirect_doi_10_1016_j_cagd_2004_04_003 |
| PublicationCentury | 2000 |
| PublicationDate | 2004-07-01 |
| PublicationDateYYYYMMDD | 2004-07-01 |
| PublicationDate_xml | – month: 07 year: 2004 text: 2004-07-01 day: 01 |
| PublicationDecade | 2000 |
| PublicationTitle | Computer aided geometric design |
| PublicationYear | 2004 |
| Publisher | Elsevier B.V Elsevier |
| Publisher_xml | – name: Elsevier B.V – name: Elsevier |
| References | Prautzsch, Umlauf (BIB017) 1998 Umlauf G., 1999. Glatte FreiformflSchen und optimierte Unterteilungsalgorithmen. PhD thesis. University of Karlsruhe, Germany (in German) Alvarez, Cominetti (BIB001) 2002; 93 Kobbelt (BIB009) 1996 Peters, Reif (BIB014) 1998; 35 Sabin, Barthe (BIB022) 2002 Kobbelt (BIB010) 2000 Catmull, Clark (BIB003) 1978; 10 Ball, Storry (BIB002) 1988; 7 Prautzsch (BIB016) 1998; 14 Loop C., 1987. Smooth subdivision surfaces based on triangles. Master's thesis. University of Utah Stam (BIB023) 1998 Sabin (BIB021) 2002 Velho, Zorin (BIB020) 2001; 18 Warren, Weimer (BIB026) 2002 Zorin D., 1997. Stationary subdivision and multiresolution surface representations. PhD thesis. Caltech, Pasadena, California Doo, Sabin (BIB005) 1978; 10 Zorin, Schröder (BIB030) 2001; 18 de Boor, Hollig, Riemenschneider (BIB004) 1994 Gerot, Barthe, Dodgson, Sabin (BIB008) 2004 Ron A., 2000. Private communication Dyn (BIB006) 1992 Farin (BIB007) 2002 Stam (BIB024) 2001; 18 Zorin D., Schröder P., 2000. Subdivision for modeling and animation. SIGGRAPH 2000 course notes Reif (BIB018) 1995; 12 Zorin (BIB029) 2000; 35 Loop (BIB012) 2002; 18 Peters, Reif (BIB013) 1997; 16 Peters, Umlauf (BIB015) 2001; 18 Ball (10.1016/j.cagd.2004.04.003_BIB002) 1988; 7 Doo (10.1016/j.cagd.2004.04.003_BIB005) 1978; 10 10.1016/j.cagd.2004.04.003_BIB028 Zorin (10.1016/j.cagd.2004.04.003_BIB029) 2000; 35 Catmull (10.1016/j.cagd.2004.04.003_BIB003) 1978; 10 Peters (10.1016/j.cagd.2004.04.003_BIB015) 2001; 18 Stam (10.1016/j.cagd.2004.04.003_BIB023) 1998 10.1016/j.cagd.2004.04.003_BIB027 Farin (10.1016/j.cagd.2004.04.003_BIB007) 2002 Prautzsch (10.1016/j.cagd.2004.04.003_BIB016) 1998; 14 Sabin (10.1016/j.cagd.2004.04.003_BIB021) 2002 10.1016/j.cagd.2004.04.003_BIB025 Kobbelt (10.1016/j.cagd.2004.04.003_BIB009) 1996 Warren (10.1016/j.cagd.2004.04.003_BIB026) 2002 Peters (10.1016/j.cagd.2004.04.003_BIB013) 1997; 16 Alvarez (10.1016/j.cagd.2004.04.003_BIB001) 2002; 93 Peters (10.1016/j.cagd.2004.04.003_BIB014) 1998; 35 Stam (10.1016/j.cagd.2004.04.003_BIB024) 2001; 18 10.1016/j.cagd.2004.04.003_BIB019 Loop (10.1016/j.cagd.2004.04.003_BIB012) 2002; 18 Zorin (10.1016/j.cagd.2004.04.003_BIB030) 2001; 18 Sabin (10.1016/j.cagd.2004.04.003_BIB022) 2002 Prautzsch (10.1016/j.cagd.2004.04.003_BIB017) 1998 10.1016/j.cagd.2004.04.003_BIB011 Reif (10.1016/j.cagd.2004.04.003_BIB018) 1995; 12 Velho (10.1016/j.cagd.2004.04.003_BIB020) 2001; 18 Dyn (10.1016/j.cagd.2004.04.003_BIB006) 1992 Kobbelt (10.1016/j.cagd.2004.04.003_BIB010) 2000 Gerot (10.1016/j.cagd.2004.04.003_BIB008) 2004 de Boor (10.1016/j.cagd.2004.04.003_BIB004) 1994 |
| References_xml | – year: 1994 ident: BIB004 article-title: Box Splines contributor: fullname: Riemenschneider – volume: 10 start-page: 350 year: 1978 end-page: 355 ident: BIB003 article-title: Recursively generated B-spline surfaces on arbitrary topological meshes publication-title: Computer-Aided Design contributor: fullname: Clark – volume: 35 start-page: 728 year: 1998 end-page: 748 ident: BIB014 article-title: Analysis of algorithms generalizing B-spline subdivision publication-title: SIAM J. Numer. Anal. contributor: fullname: Reif – volume: 14 start-page: 377 year: 1998 end-page: 390 ident: BIB016 article-title: Smoothness of subdivision surfaces at extraordinary points publication-title: Adv. Comp. Math. contributor: fullname: Prautzsch – volume: 35 start-page: 1677 year: 2000 end-page: 1708 ident: BIB029 article-title: A method for analysis of publication-title: SIAM J. Numer. Anal. contributor: fullname: Zorin – year: 2002 ident: BIB022 article-title: Artifact in recursive subdivision surfaces publication-title: Curves and Surfaces 2002 Proceedings contributor: fullname: Barthe – start-page: 395 year: 1998 end-page: 404 ident: BIB023 article-title: Exact evaluation of Catmull–Clark subdivision surfaces at arbitrary parameter values publication-title: Proceedings of SIGGRAPH 1998, Computer Graphics Proceedings, Annual Conference Series contributor: fullname: Stam – volume: 16 start-page: 420 year: 1997 end-page: 431 ident: BIB013 article-title: The simplest subdivision scheme for smoothing polyhedra publication-title: ACM Trans. Graph. contributor: fullname: Reif – volume: 18 start-page: 383 year: 2001 end-page: 396 ident: BIB024 article-title: On subdivision schemes generalizing uniform B-spline surfaces of arbitrary degree publication-title: Computer Aided Geometric Design (Special issue on subdivision surfaces) contributor: fullname: Stam – volume: 18 start-page: 455 year: 2001 end-page: 461 ident: BIB015 article-title: Computing curvature bounds for bounded curvature subdivision publication-title: Computer Aided Geometric Design (Special issue on subdivision surfaces) contributor: fullname: Umlauf – volume: 18 start-page: 397 year: 2001 end-page: 428 ident: BIB020 article-title: 4–8 subdivision publication-title: Computer Aided Geometric Design (Special issue on subdivision surfaces) contributor: fullname: Zorin – year: 2002 ident: BIB026 article-title: Subdivision Methods for Geometric Design: A Constructive Approach contributor: fullname: Weimer – start-page: 103 year: 2000 end-page: 112 ident: BIB010 article-title: publication-title: Proceedings of SIGGRAPH 2000, Computer Graphics Proceedings, Annual Conference Series contributor: fullname: Kobbelt – volume: 18 start-page: 429 year: 2001 end-page: 454 ident: BIB030 article-title: A unified framework for primal/dual quadrilateral subdivision schemes publication-title: Computer Aided Geometric Design (Special issue on subdivision surfaces) contributor: fullname: Schröder – year: 2002 ident: BIB007 article-title: CAGD a Practical Guide contributor: fullname: Farin – volume: 18 start-page: 316 year: 2002 end-page: 325 ident: BIB012 article-title: Bounded curvature triangular mesh subdivision with the convex hull property publication-title: The Visual Computer contributor: fullname: Loop – start-page: 69 year: 2002 end-page: 97 ident: BIB021 article-title: Eigenanalysis and artifacts of subdivision curves and surfaces publication-title: Tutorial on Multiresolution in Geometric Modelling contributor: fullname: Sabin – start-page: 217 year: 1998 end-page: 224 ident: BIB017 article-title: A publication-title: Geometric Modelling contributor: fullname: Umlauf – year: 2004 ident: BIB008 article-title: Subdivision as a sequence of sampled Cp surfaces publication-title: Proc. of MINGLE Workshop, September 2003 contributor: fullname: Sabin – volume: 10 start-page: 356 year: 1978 end-page: 360 ident: BIB005 article-title: Analysis of the behaviour of recursive subdivision surfaces near extraordinary points publication-title: Computer-Aided Design contributor: fullname: Sabin – start-page: 409 year: 1996 end-page: 420 ident: BIB009 article-title: Interpolatory subdivision on open quadrilateral nets with arbitrary topology publication-title: Computer Graphics Forum 15, Eurographics '96 issue contributor: fullname: Kobbelt – volume: 7 start-page: 83 year: 1988 end-page: 102 ident: BIB002 article-title: Conditions for tangent plane continuity over recursively generated B-spline surfaces publication-title: ACM Trans. Graph. contributor: fullname: Storry – start-page: 36 year: 1992 end-page: 104 ident: BIB006 article-title: Subdivision schemes in computer-aided geometric design publication-title: Advances in Numerical Analysis, II, Wavelets, Subdivision Algorithms and Radial Basis Functions contributor: fullname: Dyn – volume: 12 start-page: 153 year: 1995 end-page: 174 ident: BIB018 article-title: A unified approach to subdivision algorithms near extraordinary vertices publication-title: Computer-Aided Design contributor: fullname: Reif – volume: 93 start-page: 87 year: 2002 end-page: 96 ident: BIB001 article-title: Primal and dual convergence of a proximal point exponential penalty method for linear programming publication-title: Math. Programming contributor: fullname: Cominetti – volume: 35 start-page: 728 issue: 2 year: 1998 ident: 10.1016/j.cagd.2004.04.003_BIB014 article-title: Analysis of algorithms generalizing B-spline subdivision publication-title: SIAM J. Numer. Anal. doi: 10.1137/S0036142996304346 contributor: fullname: Peters – volume: 7 start-page: 83 issue: 2 year: 1988 ident: 10.1016/j.cagd.2004.04.003_BIB002 article-title: Conditions for tangent plane continuity over recursively generated B-spline surfaces publication-title: ACM Trans. Graph. doi: 10.1145/42458.42459 contributor: fullname: Ball – volume: 18 start-page: 455 issue: 5 year: 2001 ident: 10.1016/j.cagd.2004.04.003_BIB015 article-title: Computing curvature bounds for bounded curvature subdivision publication-title: Computer Aided Geometric Design (Special issue on subdivision surfaces) doi: 10.1016/S0167-8396(01)00041-3 contributor: fullname: Peters – ident: 10.1016/j.cagd.2004.04.003_BIB027 – volume: 12 start-page: 153 year: 1995 ident: 10.1016/j.cagd.2004.04.003_BIB018 article-title: A unified approach to subdivision algorithms near extraordinary vertices publication-title: Computer-Aided Design doi: 10.1016/0167-8396(94)00007-F contributor: fullname: Reif – year: 2002 ident: 10.1016/j.cagd.2004.04.003_BIB026 contributor: fullname: Warren – ident: 10.1016/j.cagd.2004.04.003_BIB019 – volume: 14 start-page: 377 year: 1998 ident: 10.1016/j.cagd.2004.04.003_BIB016 article-title: Smoothness of subdivision surfaces at extraordinary points publication-title: Adv. Comp. Math. doi: 10.1023/A:1018945708536 contributor: fullname: Prautzsch – volume: 18 start-page: 316 issue: 5–6 year: 2002 ident: 10.1016/j.cagd.2004.04.003_BIB012 article-title: Bounded curvature triangular mesh subdivision with the convex hull property publication-title: The Visual Computer doi: 10.1007/s003710100148 contributor: fullname: Loop – volume: 18 start-page: 383 issue: 5 year: 2001 ident: 10.1016/j.cagd.2004.04.003_BIB024 article-title: On subdivision schemes generalizing uniform B-spline surfaces of arbitrary degree publication-title: Computer Aided Geometric Design (Special issue on subdivision surfaces) doi: 10.1016/S0167-8396(01)00038-3 contributor: fullname: Stam – volume: 18 start-page: 397 issue: 5 year: 2001 ident: 10.1016/j.cagd.2004.04.003_BIB020 article-title: 4–8 subdivision publication-title: Computer Aided Geometric Design (Special issue on subdivision surfaces) doi: 10.1016/S0167-8396(01)00039-5 contributor: fullname: Velho – start-page: 36 year: 1992 ident: 10.1016/j.cagd.2004.04.003_BIB006 article-title: Subdivision schemes in computer-aided geometric design contributor: fullname: Dyn – volume: 93 start-page: 87 issue: 1 year: 2002 ident: 10.1016/j.cagd.2004.04.003_BIB001 article-title: Primal and dual convergence of a proximal point exponential penalty method for linear programming publication-title: Math. Programming doi: 10.1007/s10107-002-0295-0 contributor: fullname: Alvarez – year: 2002 ident: 10.1016/j.cagd.2004.04.003_BIB007 contributor: fullname: Farin – volume: 35 start-page: 1677 issue: 5 year: 2000 ident: 10.1016/j.cagd.2004.04.003_BIB029 article-title: A method for analysis of C1-continuity of subdivision surfaces publication-title: SIAM J. Numer. Anal. doi: 10.1137/S003614299834263X contributor: fullname: Zorin – ident: 10.1016/j.cagd.2004.04.003_BIB011 – year: 2004 ident: 10.1016/j.cagd.2004.04.003_BIB008 article-title: Subdivision as a sequence of sampled Cp surfaces contributor: fullname: Gerot – volume: 18 start-page: 429 issue: 5 year: 2001 ident: 10.1016/j.cagd.2004.04.003_BIB030 article-title: A unified framework for primal/dual quadrilateral subdivision schemes publication-title: Computer Aided Geometric Design (Special issue on subdivision surfaces) doi: 10.1016/S0167-8396(01)00040-1 contributor: fullname: Zorin – start-page: 217 year: 1998 ident: 10.1016/j.cagd.2004.04.003_BIB017 article-title: A G2-subdivision algorithm contributor: fullname: Prautzsch – year: 2002 ident: 10.1016/j.cagd.2004.04.003_BIB022 article-title: Artifact in recursive subdivision surfaces contributor: fullname: Sabin – ident: 10.1016/j.cagd.2004.04.003_BIB028 – volume: 16 start-page: 420 issue: 4 year: 1997 ident: 10.1016/j.cagd.2004.04.003_BIB013 article-title: The simplest subdivision scheme for smoothing polyhedra publication-title: ACM Trans. Graph. doi: 10.1145/263834.263851 contributor: fullname: Peters – year: 1994 ident: 10.1016/j.cagd.2004.04.003_BIB004 contributor: fullname: de Boor – start-page: 395 year: 1998 ident: 10.1016/j.cagd.2004.04.003_BIB023 article-title: Exact evaluation of Catmull–Clark subdivision surfaces at arbitrary parameter values contributor: fullname: Stam – start-page: 69 year: 2002 ident: 10.1016/j.cagd.2004.04.003_BIB021 article-title: Eigenanalysis and artifacts of subdivision curves and surfaces contributor: fullname: Sabin – start-page: 103 year: 2000 ident: 10.1016/j.cagd.2004.04.003_BIB010 article-title: 3-Subdivision contributor: fullname: Kobbelt – volume: 10 start-page: 356 issue: 6 year: 1978 ident: 10.1016/j.cagd.2004.04.003_BIB005 article-title: Analysis of the behaviour of recursive subdivision surfaces near extraordinary points publication-title: Computer-Aided Design doi: 10.1016/0010-4485(78)90111-2 contributor: fullname: Doo – ident: 10.1016/j.cagd.2004.04.003_BIB025 – volume: 10 start-page: 350 issue: 6 year: 1978 ident: 10.1016/j.cagd.2004.04.003_BIB003 article-title: Recursively generated B-spline surfaces on arbitrary topological meshes publication-title: Computer-Aided Design doi: 10.1016/0010-4485(78)90110-0 contributor: fullname: Catmull – start-page: 409 year: 1996 ident: 10.1016/j.cagd.2004.04.003_BIB009 article-title: Interpolatory subdivision on open quadrilateral nets with arbitrary topology contributor: fullname: Kobbelt |
| SSID | ssj0002196 |
| Score | 1.8807108 |
| Snippet | In this paper we extend the standard method to derive and optimize subdivision rules in the vicinity of extraordinary vertices (EV). Starting from a given set... |
| SourceID | hal crossref elsevier |
| SourceType | Open Access Repository Aggregation Database Publisher |
| StartPage | 561 |
| SubjectTerms | Computer Science Extraordinary vertices Graphics Meshes Subdivision surfaces |
| Title | Subdivision scheme tuning around extraordinary vertices |
| URI | https://dx.doi.org/10.1016/j.cagd.2004.04.003 https://hal.science/hal-01538452 |
| Volume | 21 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://sdu.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV3dT9swELcGvMADYgMEg03RxFsUKYkdx37stqJu2ngBJN4if4UP0XYqLX8_d7GTtiAQTEKqotZK7Mh3-vnuevc7Qo40Z8JwWSe1LkzCFNWJlFonuU4Ns9YWuikfG5yWJxfiZ5_15-2O5mPvKmkYA1lj5ewbpN1NCgPwHWQOV5A6XF8ld0ACLLHCIFgMnqsbung6a4IfaoItlGJA44kCl9MX4jbtmE1IJGwZC0KnhxjpI2186cZD7LtlYruU7vEdVr_yfZrHzf_tx6aD77HW7tY7_e66XgotsC4NNcS7ntS8-BAkQCuYVYHA2sOmKGWSU7qEq77yOejPIkgWnn49nLeFb2TzBMp9VOEG3PTLhtGVNZS0KZ0fXF064Sm-E74SIlLKkfx1LQfgAdxb6_3qX_zuzmbAZ96yveMDoYzKZ_w9Xuk5U2Xlqg26N0bI2RbZDN5D1PNi_0g-uNEnsrHAKQm__nZEvHfbpFxQh8irQ-TVIfLqEC2pQ9Sqww45P-6f_RgkoVdGYuCImCZZXhusTFO8lBml1oJZrG2d1aW2KlWCl9xyY8EbdsKJHKzWrBROukyKTJVG0l2yOhqP3B6JBBXKIi-klpTBFHA3dVLJtOYa_AW6T-J2W6p_nhKlanMFbyrcROxtyir8pHB30e5cFYw6b6xVIOgXn_sG29wtgCzog96fCsdSPKVZkd9nn_9z8gOyPtf3Q7I6nczcF7JyZ2dfg8Y8AKIteDU |
| link.rule.ids | 230,315,782,786,887,27933,27934 |
| linkProvider | Elsevier |
| 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=Subdivision+scheme+tuning+around+extraordinary+vertices&rft.jtitle=Computer+aided+geometric+design&rft.au=Barthe%2C+Lo%C3%AFc&rft.au=Kobbelt%2C+Leif&rft.date=2004-07-01&rft.pub=Elsevier+B.V&rft.issn=0167-8396&rft.eissn=1879-2332&rft.volume=21&rft.issue=6&rft.spage=561&rft.epage=583&rft_id=info:doi/10.1016%2Fj.cagd.2004.04.003&rft.externalDocID=S0167839604000603 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0167-8396&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0167-8396&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0167-8396&client=summon |