Reconstruction of the initial curve from a two-dimensional shape for the B-spline curve fitting

Curve reconstruction is a significant challenge in computer-aided geometric design, computational atomic and molecular physics, engineering design, virtual reality and data visualization. This study discusses a method of producing B-spline parametric curve from the large number of data points. The i...

Celý popis

Uložené v:

Podrobná bibliografia
Vydané v:	European physical journal plus Ročník 137; číslo 3; s. 411
Hlavní autori:	Jahanshahloo, Almas, Ebrahimi, ALireza
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Berlin/Heidelberg Springer Berlin Heidelberg 31.03.2022 Springer Nature B.V
Predmet:	Algorithms Applied and Technical Physics Approximation Atomic B spline functions CAD Complex Systems Computer aided design Condensed Matter Physics Cultural heritage Curve fitting Data compression Data points Design engineering Error reduction Identification methods Mathematical and Computational Physics Molecular Molecular physics Optical and Plasma Physics Optimization techniques Parameter estimation Parameter identification Physics Physics and Astronomy Production methods Reconstruction Regular Article Scientific visualization Theoretical Video compression Virtual reality Water waves
ISSN:	2190-5444, 2190-5444
On-line prístup:	Získať plný text
Tagy:	Pridať tag Žiadne tagy, Buďte prvý, kto otaguje tento záznam!

Abstract	Curve reconstruction is a significant challenge in computer-aided geometric design, computational atomic and molecular physics, engineering design, virtual reality and data visualization. This study discusses a method of producing B-spline parametric curve from the large number of data points. The introduced scheme includes three major parts for curve reconstruction: (1) formulation of the B-spline curve fitting as a nonlinear least squares optimization problem, (2) construction of the precise initial B-spline curve using properly determined control points, and (3) usage of the diagonal approximation BFGS method to identify the location parameters and the control points simultaneously. The modeling examples demonstrate that the suggested techniques are successful and can therefore significantly reduce fitting error by adjusting the number and location of control points.
AbstractList	Curve reconstruction is a significant challenge in computer-aided geometric design, computational atomic and molecular physics, engineering design, virtual reality and data visualization. This study discusses a method of producing B-spline parametric curve from the large number of data points. The introduced scheme includes three major parts for curve reconstruction: (1) formulation of the B-spline curve fitting as a nonlinear least squares optimization problem, (2) construction of the precise initial B-spline curve using properly determined control points, and (3) usage of the diagonal approximation BFGS method to identify the location parameters and the control points simultaneously. The modeling examples demonstrate that the suggested techniques are successful and can therefore significantly reduce fitting error by adjusting the number and location of control points.
ArticleNumber	411
Author	Jahanshahloo, Almas Ebrahimi, ALireza
Author_xml	– sequence: 1 givenname: Almas surname: Jahanshahloo fullname: Jahanshahloo, Almas organization: Department of Mathematics, East Tehran Branch, Islamic Azad University – sequence: 2 givenname: ALireza surname: Ebrahimi fullname: Ebrahimi, ALireza email: a.ebrahimi@stu.yazd.ac.ir, a.ebrahimi65@gmail.com organization: Computer Geometry and Dynamical Systems Laboratory, Faculty of Mathematical Sciences, Yazd University
BookMark	eNqNkF1LQyEYxyUKWmufoQNd29TjPMeLLmr0BoMg6lo8TjfHpif1FPv2uZ2i6KYEX-D5__TxdwIOnXcagDOMLjCmaKzbVTuOuCwZgoiQPBmicHsABgRzBCeU0sMf52MwinGF8qAcU04HQDxp5V1MoVPJeld4U6SlLqyzycp1obrwpgsT_KaQRXr3cG432sWczMW4lG0u-rBHrmFs19bpL8amZN3iFBwZuY569LkPwcvtzfP0Hs4e7x6mVzOoCKMJMs6bms15qVhjOEaENvknmmmOKlpjiWXFGqImplKGE9XwuiJNbRo5MeWc5GUIzvt72-BfOx2TWPku5C6jIBxzhhEmdU5VfUoFH2PQRrTBbmTYCozETqjYCRW9UJGFir1Qsc3k5S9S2SR3ylKQdv0Pvu75mF90Cx2--_sL_QBJnpPT
CitedBy_id	crossref_primary_10_1108_EC_11_2022_0666 crossref_primary_10_1016_j_measurement_2023_114089 crossref_primary_10_1177_09544054241292120 crossref_primary_10_1007_s11431_023_2617_3 crossref_primary_10_1016_j_oceaneng_2023_115610 crossref_primary_10_1063_5_0131029 crossref_primary_10_1016_j_optlaseng_2025_109167 crossref_primary_10_1007_s40819_023_01630_3
Cites_doi	10.1145/344779.344849 10.1140/epjp/s13360-021-01773-6 10.1016/S0010-4485(03)00140-4 10.1016/j.aml.2020.106936 10.1088/1674-1137/33/1/006 10.1016/j.cam.2019.03.025 10.1007/978-3-642-04074-0 10.1007/978-1-84628-871-5 10.1016/j.cad.2011.01.015 10.1007/s40314-017-0487-0 10.1063/1.3257237 10.1016/j.aml.2021.107301 10.1007/s11045-014-0293-4 10.1007/s10543-012-0371-7 10.1016/j.cad.2011.11.005 10.1371/journal.pone.0179721 10.1016/j.laa.2015.01.010 10.1016/S0167-8396(98)00024-7 10.1145/1138450.1138453 10.1016/j.ast.2016.06.016 10.1016/j.chaos.2021.111222 10.1016/S0097-8493(02)00134-6 10.1007/s40314-018-0598-2 10.1016/j.cad.2011.07.010 10.1016/B978-0-12-174585-1.50026-9 10.1155/2013/528215 10.1016/S0020-0255(02)00376-6 10.1007/s11760-010-0165-9 10.1093/ietisy/e90-d.5.844 10.1140/epjp/i2019-12704-1 10.1016/j.aml.2021.107161 10.1088/0034-4885/64/12/205 10.1016/j.cagd.2012.03.004 10.1002/9781118625590 10.1016/S0007-8506(07)60066-3 10.1016/j.chaos.2020.110487 10.1088/1572-9494/aba23d 10.1016/j.imavis.2008.07.012 10.1016/j.aej.2017.01.004 10.1016/j.aej.2017.02.016 10.1007/s11042-018-6109-z 10.1016/j.chaos.2021.111066 10.1016/j.patcog.2003.09.001 10.1016/j.cad.2006.12.006 10.1007/978-3-662-53090-0_7 10.1007/s40995-017-0347-1 10.1007/s00211-002-0410-4 10.1016/j.cma.2019.03.035 10.1179/136821910X12750339175709 10.1007/978-3-642-78114-8_29 10.1088/1742-6596/1748/5/052036
ContentType	Journal Article
Copyright	The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022 The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022.
Copyright_xml	– notice: The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022 – notice: The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022.
DBID	AAYXX CITATION 8FE 8FG AEUYN AFKRA ARAPS BENPR BGLVJ BHPHI BKSAR CCPQU DWQXO HCIFZ P5Z P62 PCBAR PHGZM PHGZT PKEHL PQEST PQGLB PQQKQ PQUKI
DOI	10.1140/epjp/s13360-022-02604-y
DatabaseName	CrossRef ProQuest SciTech Collection ProQuest Technology Collection One Sustainability ProQuest Central UK/Ireland Advanced Technologies & Computer Science Collection ProQuest Central Technology Collection Natural Science Collection Earth, Atmospheric & Aquatic Science Collection ProQuest One Community College ProQuest Central Korea SciTech Premium Collection Advanced Technologies & Aerospace Database ProQuest Advanced Technologies & Aerospace Collection Earth, Atmospheric & Aquatic Science Database ProQuest Central Premium ProQuest One Academic (New) ProQuest One Academic Middle East (New) ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Applied & Life Sciences ProQuest One Academic (retired) ProQuest One Academic UKI Edition
DatabaseTitle	CrossRef Advanced Technologies & Aerospace Collection Technology Collection ProQuest One Academic Middle East (New) ProQuest Advanced Technologies & Aerospace Collection ProQuest One Academic Eastern Edition Earth, Atmospheric & Aquatic Science Database SciTech Premium Collection ProQuest One Community College ProQuest Technology Collection ProQuest SciTech Collection Earth, Atmospheric & Aquatic Science Collection ProQuest Central Advanced Technologies & Aerospace Database ProQuest One Applied & Life Sciences ProQuest One Sustainability ProQuest One Academic UKI Edition Natural Science Collection ProQuest Central Korea ProQuest Central (New) ProQuest One Academic ProQuest One Academic (New)
DatabaseTitleList	Advanced Technologies & Aerospace Collection
Database_xml	– sequence: 1 dbid: P5Z name: Advanced Technologies & Aerospace Database url: https://search.proquest.com/hightechjournals sourceTypes: Aggregation Database
DeliveryMethod	fulltext_linktorsrc
Discipline	Physics
EISSN	2190-5444
ExternalDocumentID	10_1140_epjp_s13360_022_02604_y
GroupedDBID	-5F -5G -BR -EM -~C 06D 0R~ 203 29~ 2JN 2KG 30V 4.4 406 408 8UJ 95. 96X AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYTO AAYZH AAZMS ABAKF ABDZT ABECU ABFTV ABHLI ABJNI ABJOX ABKCH ABMQK ABQBU ABSXP ABTEG ABTHY ABTKH ABTMW ABXPI ACAOD ACDTI ACGFS ACHSB ACKNC ACMDZ ACMLO ACOKC ACPIV ACREN ACZOJ ADHHG ADINQ ADKNI ADKPE ADURQ ADYFF ADZKW AEFQL AEGNC AEJHL AEJRE AEMSY AENEX AEOHA AEPYU AESKC AETCA AEUYN AEVLU AEXYK AFBBN AFKRA AFQWF AFWTZ AFZKB AGAYW AGDGC AGMZJ AGQEE AGQMX AGRTI AGWZB AGYKE AHAVH AHBYD AHYZX AIAKS AIGIU AIIXL AILAN AITGF AJRNO AJZVZ ALFXC ALMA_UNASSIGNED_HOLDINGS AMKLP AMXSW AMYLF AMYQR ANMIH AOCGG ARAPS ARMRJ AXYYD AYJHY BENPR BGLVJ BGNMA BHPHI BKSAR CCPQU CSCUP DDRTE DNIVK DPUIP EBLON EBS EIOEI ESBYG FERAY FFXSO FIGPU FNLPD FRRFC GGCAI GGRSB GJIRD GNWQR GQ6 GQ7 HCIFZ HMJXF HRMNR HZ~ I0C IKXTQ IWAJR IXD J-C JBSCW JZLTJ KOV LLZTM M4Y NPVJJ NQJWS NU0 O93 O9J P9T PCBAR PT4 RID RLLFE ROL RSV S27 S3B SHX SISQX SJYHP SNE SNPRN SNX SOHCF SOJ SPH SPISZ SRMVM SSLCW STPWE SZN T13 TSG U2A UG4 UOJIU UTJUX UZXMN VC2 VFIZW W48 WK8 Z7S Z7Y ZMTXR ~A9 AAPKM AAYXX ABBRH ABDBE ABFSG ABRTQ ACSTC AEZWR AFDZB AFFHD AFHIU AFOHR AHPBZ AHWEU AIXLP ATHPR AYFIA CITATION PHGZM PHGZT PQGLB 8FE 8FG DWQXO P62 PKEHL PQEST PQQKQ PQUKI
ID	FETCH-LOGICAL-c264t-699b86d93c6bf91024b260e6e907481a1a76b2c5f7cf92cb9872b8fba5f3d25f3
IEDL.DBID	P5Z
ISICitedReferencesCount	8
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000776729400002&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN	2190-5444
IngestDate	Wed Nov 05 04:25:28 EST 2025 Sat Nov 29 03:58:21 EST 2025 Tue Nov 18 21:50:47 EST 2025 Fri Feb 21 02:47:28 EST 2025
IsPeerReviewed	true
IsScholarly	true
Issue	3
Language	English
LinkModel	DirectLink
MergedId	FETCHMERGED-LOGICAL-c264t-699b86d93c6bf91024b260e6e907481a1a76b2c5f7cf92cb9872b8fba5f3d25f3
Notes	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
PQID	2919610128
PQPubID	2044220
ParticipantIDs	proquest_journals_2919610128 crossref_primary_10_1140_epjp_s13360_022_02604_y crossref_citationtrail_10_1140_epjp_s13360_022_02604_y springer_journals_10_1140_epjp_s13360_022_02604_y
PublicationCentury	2000
PublicationDate	2022-03-31
PublicationDateYYYYMMDD	2022-03-31
PublicationDate_xml	– month: 03 year: 2022 text: 2022-03-31 day: 31
PublicationDecade	2020
PublicationPlace	Berlin/Heidelberg
PublicationPlace_xml	– name: Berlin/Heidelberg – name: Heidelberg
PublicationTitle	European physical journal plus
PublicationTitleAbbrev	Eur. Phys. J. Plus
PublicationYear	2022
Publisher	Springer Berlin Heidelberg Springer Nature B.V
Publisher_xml	– name: Springer Berlin Heidelberg – name: Springer Nature B.V
References	ZhengWBoPLiuYWangWFast B-spline curve fitting by L-BFGSComput. Aided Geom. Des.201229744846229259481250.65022 GaoXYGuoYJShanWRBilinear forms through the binary Bell polynomials, N solitons and Bäcklund transformations of the Boussinesq–Burgers system for the shallow water waves in a lake or near an ocean beachCommun. Theor. Phys.20207290950022020CoTPh..72i5002G1451.76023 ZieniukEKapturczakMModeling the shape of boundary using NURBS curves directly in modified boundary integral equations for Laplace’s equationComput. Appl. Math.20183744835485538485681432.65020 PatrikalakisNMMaekawaTShape Interrogation for Computer Aided Design and Manufacturing2002BerlinSpringer1035.65016 MasoodASarfrazMCapturing outlines of 2D objects with Bézier cubic approximationImage Vis. Comput.2009276704712 M.G. Cox, Algorithms for spline curves and surfaces. NPL Report (1990) DraperNRSmithHApplied Regression Analysis1998HobokenWiley0895.62073 ZhaoXZhangCYangBLiPAdaptive knot placement using a GMM-based continuous optimization algorithm in B-spline curve approximationComput.-Aided Des.20114365986042011icai.conf.....Z KhanMAA new method for video data compression by quadratic Bézier curve fittingSignal Image Video Process.2012611924 BergströmPSöderkvistIFitting NURBS using separable least squares techniquesInt. J. Math. Model. Numer. Optim.2012343193341259.65018 SarfrazMInteractive Curve Modeling2008BerlinSpringer GallierJGallierJHCurves and Surfaces in Geometric Modeling: Theory and Algorithms2000Burlington, MAMorgan Kaufmann0988.65008 N. Carlson, M. Gulliksson, S. Kartalopoulos, A. Buikis, N. Mastorakis, L. Vladareanu, Surface fitting with NURBS—a Gauss Newton with trust region approach. In: WSEAS International Conference. Proceedings. Mathematics and Computers in Science and Engineering (No. 13). WSEAS; (2008) GálvezAIglesiasAParticle-based meta-model for continuous breakpoint optimization in smooth local-support curve fittingAppl. Math. Comput.201627519521234377021410.90260 WeberJHansenTVan de SandenMEngelnRB-spline parametrization of the dielectric function applied to spectroscopic ellipsometry on amorphous carbonJ. Appl. Phys.2009106121235032009JAP...106l3503W LeuMPengXZhangWSurface reconstruction for interactive modeling of freeform solids by virtual sculptingCIRP Ann.2005541131134 EbrahimiALoghmaniGBShape modeling based on specifying the initial B-spline curve and scaled BFGS optimization methodMultimedia Tools Appl.201877233033130351 GálvezAIglesiasAEfficient particle swarm optimization approach for data fitting with free knot B-splinesComput.-Aided Des.2011431216831692 SarfrazMSamreenSHussainMZA quadratic trigonometric weighted spline with local support basis functionsAlex. Eng. J.201857210411049 LiXSederbergTWS-splines: a simple surface solution for IGA and CADComput. Methods Appl. Mech. Eng.20193506646782019CMAME.350..664L39339731441.65015 SunWYuanYXOptimization Theory and Methods: Nonlinear Programming2006BerlinSpringer1129.90002 MajeedAYahyaZRAbdullahJYRafiqueMConstruction of occipital bone fracture using B-spline curvesComput. Appl. Math.20183732877289638260141471.92180 SarfrazMRazzakFA Web based system to capture outlines of Arabic fontsInf. Sci.20031503–4177193 AbbasSHussainMZIrshadMImage interpolation by rational ball cubic B-spline representation and genetic algorithmAlex. Eng. J.2018572931937 SalomonDCurves and Surfaces for Computer Graphics2007BerlinSpringer1083.65022 WangWPottmannHLiuYFitting B-spline curves to point clouds by curvature-based squared distance minimizationACM Trans. Graph. (ToG)2006252214238 M. Sarfraz, S.A. Raza, Capturing outline of fonts using genetic algorithm and splines. In: Proceedings Fifth International Conference on Information Visualisation. IEEE; (2001). p. 738–743 BiswasSOne-dimensional B–B polynomial and Hilbert scan for graylevel image codingPattern Recognit.20043747898002004PatRe..37..789B1067.68777 EbrahimiABarid LoghmaniGSarfrazMCapturing outlines of generic shapes with cubic Bézier curves using the Nelder–Mead simplex methodIran. J. Numer. Anal. Optim.20199210312107497043 MasoodAEjazSOptimal curve fitting approach to represent outlines of 2D shapesImaging Sci. J.2010586308320 PieglLTillerWThe NURBS book.[Sl]: Springer Science & Business MediaCitado201263439 RossignacJBorrelPFalcidienoBKuniiTLMulti-resolution 3D approximations for rendering complex scenesModeling in Computer Graphics1993BerlinSpringer455465 ParkHLeeJHB-spline curve fitting based on adaptive curve refinement using dominant pointsComput.-Aided Des.2007396439451 Pérez-ArribasFCastañeda-SabadellIAutomatic modelling of airfoil data pointsAerosp. Sci. Technol.201655449457 BergströmPEdlundOSöderkvistIEfficient computation of the Gauss–Newton direction when fitting NURBS using ODRBIT Numer. Math.201252357158829652921255.65039 WangMTianBHuCCLiuSHGeneralized Darboux transformation, solitonic interactions and bound states for a coupled fourth-order nonlinear Schrödinger system in a birefringent optical fiberAppl. Math. Lett.20211191069361478.78067 EbadiMEbrahimiAVideo data compression by progressive iterative approximationInt. J. Interact. Multimedia Artif. Intell.202166189196 KeeCLeeSB-spline scale-space of spline curves and surfacesComput.-Aided Des.2012444275288 KhanMAAn efficient algorithm for compression of motion capture signal using multidimensional quadratic Bézier curve break-and-fit methodMultidimens. Syst. Signal Process.201627112114334413811380.94056 M. Levoy, K. Pulli, B. Curless, S. Rusinkiewicz, D. Koller, L. Pereira, et al. The digital Michelangelo project: 3D scanning of large statues. In: Proceedings of the 27th annual conference on Computer graphics and interactive techniques; (2000). p. 131–144 EbrahimiALoghmaniGBA composite iterative procedure with fast convergence rate for the progressive-iteration approximation of curvesJ. Comput. Appl. Math.201935911539359801416.65057 SarfrazMRazzakMAn algorithm for automatic capturing of the font outlinesComput. Graph.2002265795804 ShenYTianBBilinear auto-Bäcklund transformations and soliton solutions of a (3+1)-dimensional generalized nonlinear evolution equation for the shallow water wavesAppl. Math. Lett.20211221073011476.35082 FarinGEFarinGCurves and Surfaces for CAGD: A Practical Guide2002Burlington, MAMorgan Kaufmann0702.68004 JavidradFAn accelerated simulated annealing method for B-spline curve fitting to strip-shaped scattered pointsInt. J. CAD/CAM2012121919 X. Zhang, C. Yang, B-spline function modeling of electric heating flow regulating valve. In: Journal of Physics: Conference Series. vol. 1748. IOP Publishing; p. 052036 (2021) HasegawaAYTormenaCParpinelliRSBézier curve parametrization using a multiobjective evolutionary algorithmInt. J. Comput. Sci. Appl.2014112118 Meng-HuaZLiang-GangLDong-XuQZhongYAo-AoXLeast square fitting of low resolution gamma ray spectra with cubic B-spline basis functionsChin. Phys. C2009331242009ChPhC..33...54M GaoXYGuoYJShanWROptical waves/modes in a multicomponent inhomogeneous optical fiber via a three-coupled variable-coefficient nonlinear Schrödinger systemAppl. Math. Lett.20211201071611478.78057 A. Iglesias, A. Gálvez, M. Collantes, Four adaptive memetic bat algorithm schemes for Bézier curve parameterization. In: Transactions on Computational Science XXVIII. Springer; p. 127–145 (2016) KhanMAOhnoYCompression of video data using parametric line and natural cubic spline block level approximationIEICE Trans. Inf. Syst.2007905844850 NocedalJWrightSNumerical Optimization2006BerlinSpringer1104.65059 GaoXTTianBShenYFengCHComment on “Shallow water in an open sea or a wide channel: Auto-and non-auto-Bäcklund transformations with solitons for a generalized (2+1)-dimensional dispersive long-wave system.”Chaos Solitons Fractals2021151111222 GálvezAIglesiasAFirefly algorithm for explicit B-spline curve fitting to data pointsMath. Probl. Eng.2013201311231237281296.65020 YangDYTianBQuQXZhangCRChenSSWeiCCLax pair, conservation laws, Darboux transformation and localized waves of a variable-coefficient coupled Hirota system in an inhomogeneous optical fiberChaos Solitons Fractals20211501104874293639 CipollaSDi FioreCTudiscoFZelliniPAdaptive matrix algebras in unconstrained minimizationLinear Algebra Appl.201547154456833143511310.65061 SpeerTKuppeMHoschekJGlobal reparametrization for curve approximationComput. Aided Geom. Des.199815986987716471310910.68214 EbrahimiALoghmaniGBB-spline curve fitting by diagonal approximation BFGS methodsIran. J. Sci. Technol. Trans. A: Sci.20194339479583977414 YangHWangWSunJControl point adjustment for B-spline curve approximationComput.-Aided Des.2004367639652 Di FioreCFanelliSLeporeFZelliniPMatrix algebras in quasi-Newton methods for unconstrained minimizationNumer. Math.200394347950019811641034.65045 BachauHCormierEDeclevaPHansenJMartínFApplications of B-splines in atomic and molecular physicsRep. Prog. Phys.2001641218152001RPPh...64.1815B KirmaniSBilal RiazMShape preserving fractional order KNR C1 cubic splineEur. Phys. J. Plus2019134718 GaoXYGuoYJShanWRSymbolic computation on a (2+1)-dimensional generalized variable-coefficient Boiti–Leon–Pempinelli system for the water wavesChaos Solitons Fractals20211501110664281821 HussainMZAbbasSIrshadMQuadratic trigonometric B-spline for image interpolation using GAPLoS ONE2017126e0179721 BiswasSLovellBCBézier and Splines in Image Processing and Machine Vision2007BerlinSpringer1138.68061 FrankeRSchumakerLLChuiCKSchumakerLLUtrerasFIA bibliography of multivariate approximationTopics in Multivariate Approximation1987AmsterdamElsevier275335 GaoXYGuoYJShanWRLooking at an open sea via a generalized (2+1)-dimensional dispersive long-wave system for the shallow water: scaling transformations, hetero-Bäcklund transformations, bilinear forms and N solitonsEur. Phys. J. Plus2021136819 EbrahimiABarid LoghmaniGSarfrazMCapturing outlines of planar generic images by simultaneous curve fitting and sub-divisionJ. AI Data Min.202081105118 J Gallier (2604_CR2) 2000 DY Yang (2604_CR61) 2021; 150 A Masood (2604_CR23) 2010; 58 C Kee (2604_CR15) 2012; 44 A Ebrahimi (2604_CR22) 2019; 9 M Sarfraz (2604_CR13) 2018; 57 F Pérez-Arribas (2604_CR37) 2016; 55 S Biswas (2604_CR26) 2004; 37 M Wang (2604_CR58) 2021; 119 XT Gao (2604_CR60) 2021; 151 S Cipolla (2604_CR7) 2015; 471 NM Patrikalakis (2604_CR36) 2002 M Sarfraz (2604_CR21) 2002; 26 A Ebrahimi (2604_CR47) 2018; 77 MA Khan (2604_CR33) 2007; 90 MA Khan (2604_CR31) 2012; 6 M Ebadi (2604_CR34) 2021; 6 F Javidrad (2604_CR52) 2012; 12 GE Farin (2604_CR1) 2002 A Gálvez (2604_CR51) 2013; 2013 M Sarfraz (2604_CR3) 2008 MA Khan (2604_CR32) 2016; 27 A Gálvez (2604_CR49) 2016; 275 AY Hasegawa (2604_CR50) 2014; 11 M Leu (2604_CR39) 2005; 54 P Bergström (2604_CR43) 2012; 3 X Zhao (2604_CR54) 2011; 43 2604_CR30 A Ebrahimi (2604_CR17) 2019; 359 XY Gao (2604_CR63) 2020; 72 A Ebrahimi (2604_CR4) 2020; 8 W Wang (2604_CR11) 2006; 25 M Sarfraz (2604_CR20) 2003; 150 J Rossignac (2604_CR38) 1993 S Abbas (2604_CR25) 2018; 57 H Yang (2604_CR40) 2004; 36 A Ebrahimi (2604_CR46) 2019; 43 2604_CR8 C Di Fiore (2604_CR66) 2003; 94 W Sun (2604_CR68) 2006 D Salomon (2604_CR35) 2007 NR Draper (2604_CR12) 1998 E Zieniuk (2604_CR14) 2018; 37 XY Gao (2604_CR65) 2021; 136 J Nocedal (2604_CR67) 2006 2604_CR42 Z Meng-Hua (2604_CR56) 2009; 33 P Bergström (2604_CR10) 2012; 52 A Masood (2604_CR24) 2009; 27 T Speer (2604_CR44) 1998; 15 A Gálvez (2604_CR48) 2011; 43 S Biswas (2604_CR27) 2007 MZ Hussain (2604_CR28) 2017; 12 L Piegl (2604_CR5) 2012; 6 X Li (2604_CR16) 2019; 350 A Majeed (2604_CR29) 2018; 37 2604_CR19 H Bachau (2604_CR6) 2001; 64 W Zheng (2604_CR45) 2012; 29 2604_CR57 R Franke (2604_CR9) 1987 2604_CR53 J Weber (2604_CR55) 2009; 106 XY Gao (2604_CR62) 2021; 120 XY Gao (2604_CR64) 2021; 150 S Kirmani (2604_CR18) 2019; 134 Y Shen (2604_CR59) 2021; 122 H Park (2604_CR41) 2007; 39
References_xml	– reference: ZieniukEKapturczakMModeling the shape of boundary using NURBS curves directly in modified boundary integral equations for Laplace’s equationComput. Appl. Math.20183744835485538485681432.65020 – reference: MajeedAYahyaZRAbdullahJYRafiqueMConstruction of occipital bone fracture using B-spline curvesComput. Appl. Math.20183732877289638260141471.92180 – reference: BachauHCormierEDeclevaPHansenJMartínFApplications of B-splines in atomic and molecular physicsRep. Prog. Phys.2001641218152001RPPh...64.1815B – reference: GaoXYGuoYJShanWROptical waves/modes in a multicomponent inhomogeneous optical fiber via a three-coupled variable-coefficient nonlinear Schrödinger systemAppl. Math. Lett.20211201071611478.78057 – reference: GaoXTTianBShenYFengCHComment on “Shallow water in an open sea or a wide channel: Auto-and non-auto-Bäcklund transformations with solitons for a generalized (2+1)-dimensional dispersive long-wave system.”Chaos Solitons Fractals2021151111222 – reference: FarinGEFarinGCurves and Surfaces for CAGD: A Practical Guide2002Burlington, MAMorgan Kaufmann0702.68004 – reference: GálvezAIglesiasAFirefly algorithm for explicit B-spline curve fitting to data pointsMath. Probl. Eng.2013201311231237281296.65020 – reference: EbrahimiALoghmaniGBB-spline curve fitting by diagonal approximation BFGS methodsIran. J. Sci. Technol. Trans. A: Sci.20194339479583977414 – reference: X. Zhang, C. Yang, B-spline function modeling of electric heating flow regulating valve. In: Journal of Physics: Conference Series. vol. 1748. IOP Publishing; p. 052036 (2021) – reference: Meng-HuaZLiang-GangLDong-XuQZhongYAo-AoXLeast square fitting of low resolution gamma ray spectra with cubic B-spline basis functionsChin. Phys. C2009331242009ChPhC..33...54M – reference: HasegawaAYTormenaCParpinelliRSBézier curve parametrization using a multiobjective evolutionary algorithmInt. J. Comput. Sci. Appl.2014112118 – reference: GallierJGallierJHCurves and Surfaces in Geometric Modeling: Theory and Algorithms2000Burlington, MAMorgan Kaufmann0988.65008 – reference: GaoXYGuoYJShanWRBilinear forms through the binary Bell polynomials, N solitons and Bäcklund transformations of the Boussinesq–Burgers system for the shallow water waves in a lake or near an ocean beachCommun. Theor. Phys.20207290950022020CoTPh..72i5002G1451.76023 – reference: SunWYuanYXOptimization Theory and Methods: Nonlinear Programming2006BerlinSpringer1129.90002 – reference: CipollaSDi FioreCTudiscoFZelliniPAdaptive matrix algebras in unconstrained minimizationLinear Algebra Appl.201547154456833143511310.65061 – reference: AbbasSHussainMZIrshadMImage interpolation by rational ball cubic B-spline representation and genetic algorithmAlex. Eng. J.2018572931937 – reference: BiswasSOne-dimensional B–B polynomial and Hilbert scan for graylevel image codingPattern Recognit.20043747898002004PatRe..37..789B1067.68777 – reference: SarfrazMRazzakFA Web based system to capture outlines of Arabic fontsInf. Sci.20031503–4177193 – reference: EbrahimiABarid LoghmaniGSarfrazMCapturing outlines of generic shapes with cubic Bézier curves using the Nelder–Mead simplex methodIran. J. Numer. Anal. Optim.20199210312107497043 – reference: SarfrazMRazzakMAn algorithm for automatic capturing of the font outlinesComput. Graph.2002265795804 – reference: SarfrazMInteractive Curve Modeling2008BerlinSpringer – reference: ZhengWBoPLiuYWangWFast B-spline curve fitting by L-BFGSComput. Aided Geom. Des.201229744846229259481250.65022 – reference: SalomonDCurves and Surfaces for Computer Graphics2007BerlinSpringer1083.65022 – reference: KirmaniSBilal RiazMShape preserving fractional order KNR C1 cubic splineEur. Phys. J. Plus2019134718 – reference: PatrikalakisNMMaekawaTShape Interrogation for Computer Aided Design and Manufacturing2002BerlinSpringer1035.65016 – reference: LeuMPengXZhangWSurface reconstruction for interactive modeling of freeform solids by virtual sculptingCIRP Ann.2005541131134 – reference: Pérez-ArribasFCastañeda-SabadellIAutomatic modelling of airfoil data pointsAerosp. Sci. Technol.201655449457 – reference: ShenYTianBBilinear auto-Bäcklund transformations and soliton solutions of a (3+1)-dimensional generalized nonlinear evolution equation for the shallow water wavesAppl. Math. Lett.20211221073011476.35082 – reference: KeeCLeeSB-spline scale-space of spline curves and surfacesComput.-Aided Des.2012444275288 – reference: BiswasSLovellBCBézier and Splines in Image Processing and Machine Vision2007BerlinSpringer1138.68061 – reference: M.G. Cox, Algorithms for spline curves and surfaces. NPL Report (1990) – reference: SarfrazMSamreenSHussainMZA quadratic trigonometric weighted spline with local support basis functionsAlex. Eng. J.201857210411049 – reference: EbrahimiALoghmaniGBA composite iterative procedure with fast convergence rate for the progressive-iteration approximation of curvesJ. Comput. Appl. Math.201935911539359801416.65057 – reference: N. Carlson, M. Gulliksson, S. Kartalopoulos, A. Buikis, N. Mastorakis, L. Vladareanu, Surface fitting with NURBS—a Gauss Newton with trust region approach. In: WSEAS International Conference. Proceedings. Mathematics and Computers in Science and Engineering (No. 13). WSEAS; (2008) – reference: RossignacJBorrelPFalcidienoBKuniiTLMulti-resolution 3D approximations for rendering complex scenesModeling in Computer Graphics1993BerlinSpringer455465 – reference: WeberJHansenTVan de SandenMEngelnRB-spline parametrization of the dielectric function applied to spectroscopic ellipsometry on amorphous carbonJ. Appl. Phys.2009106121235032009JAP...106l3503W – reference: PieglLTillerWThe NURBS book.[Sl]: Springer Science & Business MediaCitado201263439 – reference: HussainMZAbbasSIrshadMQuadratic trigonometric B-spline for image interpolation using GAPLoS ONE2017126e0179721 – reference: LiXSederbergTWS-splines: a simple surface solution for IGA and CADComput. Methods Appl. Mech. Eng.20193506646782019CMAME.350..664L39339731441.65015 – reference: GaoXYGuoYJShanWRLooking at an open sea via a generalized (2+1)-dimensional dispersive long-wave system for the shallow water: scaling transformations, hetero-Bäcklund transformations, bilinear forms and N solitonsEur. Phys. J. Plus2021136819 – reference: JavidradFAn accelerated simulated annealing method for B-spline curve fitting to strip-shaped scattered pointsInt. J. CAD/CAM2012121919 – reference: GaoXYGuoYJShanWRSymbolic computation on a (2+1)-dimensional generalized variable-coefficient Boiti–Leon–Pempinelli system for the water wavesChaos Solitons Fractals20211501110664281821 – reference: M. Sarfraz, S.A. Raza, Capturing outline of fonts using genetic algorithm and splines. In: Proceedings Fifth International Conference on Information Visualisation. IEEE; (2001). p. 738–743 – reference: MasoodAEjazSOptimal curve fitting approach to represent outlines of 2D shapesImaging Sci. J.2010586308320 – reference: SpeerTKuppeMHoschekJGlobal reparametrization for curve approximationComput. Aided Geom. Des.199815986987716471310910.68214 – reference: ZhaoXZhangCYangBLiPAdaptive knot placement using a GMM-based continuous optimization algorithm in B-spline curve approximationComput.-Aided Des.20114365986042011icai.conf.....Z – reference: FrankeRSchumakerLLChuiCKSchumakerLLUtrerasFIA bibliography of multivariate approximationTopics in Multivariate Approximation1987AmsterdamElsevier275335 – reference: DraperNRSmithHApplied Regression Analysis1998HobokenWiley0895.62073 – reference: KhanMAAn efficient algorithm for compression of motion capture signal using multidimensional quadratic Bézier curve break-and-fit methodMultidimens. Syst. Signal Process.201627112114334413811380.94056 – reference: YangDYTianBQuQXZhangCRChenSSWeiCCLax pair, conservation laws, Darboux transformation and localized waves of a variable-coefficient coupled Hirota system in an inhomogeneous optical fiberChaos Solitons Fractals20211501104874293639 – reference: NocedalJWrightSNumerical Optimization2006BerlinSpringer1104.65059 – reference: KhanMAOhnoYCompression of video data using parametric line and natural cubic spline block level approximationIEICE Trans. Inf. Syst.2007905844850 – reference: EbrahimiABarid LoghmaniGSarfrazMCapturing outlines of planar generic images by simultaneous curve fitting and sub-divisionJ. AI Data Min.202081105118 – reference: BergströmPSöderkvistIFitting NURBS using separable least squares techniquesInt. J. Math. Model. Numer. Optim.2012343193341259.65018 – reference: MasoodASarfrazMCapturing outlines of 2D objects with Bézier cubic approximationImage Vis. Comput.2009276704712 – reference: KhanMAA new method for video data compression by quadratic Bézier curve fittingSignal Image Video Process.2012611924 – reference: ParkHLeeJHB-spline curve fitting based on adaptive curve refinement using dominant pointsComput.-Aided Des.2007396439451 – reference: Di FioreCFanelliSLeporeFZelliniPMatrix algebras in quasi-Newton methods for unconstrained minimizationNumer. Math.200394347950019811641034.65045 – reference: WangMTianBHuCCLiuSHGeneralized Darboux transformation, solitonic interactions and bound states for a coupled fourth-order nonlinear Schrödinger system in a birefringent optical fiberAppl. Math. Lett.20211191069361478.78067 – reference: WangWPottmannHLiuYFitting B-spline curves to point clouds by curvature-based squared distance minimizationACM Trans. Graph. (ToG)2006252214238 – reference: YangHWangWSunJControl point adjustment for B-spline curve approximationComput.-Aided Des.2004367639652 – reference: BergströmPEdlundOSöderkvistIEfficient computation of the Gauss–Newton direction when fitting NURBS using ODRBIT Numer. Math.201252357158829652921255.65039 – reference: A. Iglesias, A. Gálvez, M. Collantes, Four adaptive memetic bat algorithm schemes for Bézier curve parameterization. In: Transactions on Computational Science XXVIII. Springer; p. 127–145 (2016) – reference: EbrahimiALoghmaniGBShape modeling based on specifying the initial B-spline curve and scaled BFGS optimization methodMultimedia Tools Appl.201877233033130351 – reference: M. Levoy, K. Pulli, B. Curless, S. Rusinkiewicz, D. Koller, L. Pereira, et al. The digital Michelangelo project: 3D scanning of large statues. In: Proceedings of the 27th annual conference on Computer graphics and interactive techniques; (2000). p. 131–144 – reference: GálvezAIglesiasAEfficient particle swarm optimization approach for data fitting with free knot B-splinesComput.-Aided Des.2011431216831692 – reference: EbadiMEbrahimiAVideo data compression by progressive iterative approximationInt. J. Interact. Multimedia Artif. Intell.202166189196 – reference: GálvezAIglesiasAParticle-based meta-model for continuous breakpoint optimization in smooth local-support curve fittingAppl. Math. Comput.201627519521234377021410.90260 – ident: 2604_CR30 doi: 10.1145/344779.344849 – volume: 6 start-page: 189 issue: 6 year: 2021 ident: 2604_CR34 publication-title: Int. J. Interact. Multimedia Artif. Intell. – volume: 136 start-page: 1 issue: 8 year: 2021 ident: 2604_CR65 publication-title: Eur. Phys. J. Plus doi: 10.1140/epjp/s13360-021-01773-6 – volume: 36 start-page: 639 issue: 7 year: 2004 ident: 2604_CR40 publication-title: Comput.-Aided Des. doi: 10.1016/S0010-4485(03)00140-4 – volume: 119 start-page: 106936 year: 2021 ident: 2604_CR58 publication-title: Appl. Math. Lett. doi: 10.1016/j.aml.2020.106936 – volume: 9 start-page: 103 issue: 2 year: 2019 ident: 2604_CR22 publication-title: Iran. J. Numer. Anal. Optim. – volume: 33 start-page: 24 issue: 1 year: 2009 ident: 2604_CR56 publication-title: Chin. Phys. C doi: 10.1088/1674-1137/33/1/006 – volume: 359 start-page: 1 year: 2019 ident: 2604_CR17 publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2019.03.025 – volume-title: Shape Interrogation for Computer Aided Design and Manufacturing year: 2002 ident: 2604_CR36 doi: 10.1007/978-3-642-04074-0 – volume-title: Interactive Curve Modeling year: 2008 ident: 2604_CR3 doi: 10.1007/978-1-84628-871-5 – volume: 43 start-page: 598 issue: 6 year: 2011 ident: 2604_CR54 publication-title: Comput.-Aided Des. doi: 10.1016/j.cad.2011.01.015 – volume: 37 start-page: 2877 issue: 3 year: 2018 ident: 2604_CR29 publication-title: Comput. Appl. Math. doi: 10.1007/s40314-017-0487-0 – volume: 12 start-page: 9 issue: 1 year: 2012 ident: 2604_CR52 publication-title: Int. J. CAD/CAM – volume: 106 start-page: 123503 issue: 12 year: 2009 ident: 2604_CR55 publication-title: J. Appl. Phys. doi: 10.1063/1.3257237 – volume-title: Curves and Surfaces in Geometric Modeling: Theory and Algorithms year: 2000 ident: 2604_CR2 – volume: 122 start-page: 107301 year: 2021 ident: 2604_CR59 publication-title: Appl. Math. Lett. doi: 10.1016/j.aml.2021.107301 – volume: 27 start-page: 121 issue: 1 year: 2016 ident: 2604_CR32 publication-title: Multidimens. Syst. Signal Process. doi: 10.1007/s11045-014-0293-4 – volume: 52 start-page: 571 issue: 3 year: 2012 ident: 2604_CR10 publication-title: BIT Numer. Math. doi: 10.1007/s10543-012-0371-7 – volume: 44 start-page: 275 issue: 4 year: 2012 ident: 2604_CR15 publication-title: Comput.-Aided Des. doi: 10.1016/j.cad.2011.11.005 – volume: 12 start-page: e0179721 issue: 6 year: 2017 ident: 2604_CR28 publication-title: PLoS ONE doi: 10.1371/journal.pone.0179721 – volume: 471 start-page: 544 year: 2015 ident: 2604_CR7 publication-title: Linear Algebra Appl. doi: 10.1016/j.laa.2015.01.010 – volume-title: Bézier and Splines in Image Processing and Machine Vision year: 2007 ident: 2604_CR27 – volume: 15 start-page: 869 issue: 9 year: 1998 ident: 2604_CR44 publication-title: Comput. Aided Geom. Des. doi: 10.1016/S0167-8396(98)00024-7 – volume-title: Optimization Theory and Methods: Nonlinear Programming year: 2006 ident: 2604_CR68 – volume: 25 start-page: 214 issue: 2 year: 2006 ident: 2604_CR11 publication-title: ACM Trans. Graph. (ToG) doi: 10.1145/1138450.1138453 – volume: 55 start-page: 449 year: 2016 ident: 2604_CR37 publication-title: Aerosp. Sci. Technol. doi: 10.1016/j.ast.2016.06.016 – volume-title: Curves and Surfaces for CAGD: A Practical Guide year: 2002 ident: 2604_CR1 – volume: 151 start-page: 111222 year: 2021 ident: 2604_CR60 publication-title: Chaos Solitons Fractals doi: 10.1016/j.chaos.2021.111222 – volume: 26 start-page: 795 issue: 5 year: 2002 ident: 2604_CR21 publication-title: Comput. Graph. doi: 10.1016/S0097-8493(02)00134-6 – volume: 37 start-page: 4835 issue: 4 year: 2018 ident: 2604_CR14 publication-title: Comput. Appl. Math. doi: 10.1007/s40314-018-0598-2 – volume: 43 start-page: 1683 issue: 12 year: 2011 ident: 2604_CR48 publication-title: Comput.-Aided Des. doi: 10.1016/j.cad.2011.07.010 – start-page: 275 volume-title: Topics in Multivariate Approximation year: 1987 ident: 2604_CR9 doi: 10.1016/B978-0-12-174585-1.50026-9 – volume: 2013 start-page: 1 year: 2013 ident: 2604_CR51 publication-title: Math. Probl. Eng. doi: 10.1155/2013/528215 – volume: 11 start-page: 1 issue: 2 year: 2014 ident: 2604_CR50 publication-title: Int. J. Comput. Sci. Appl. – volume: 150 start-page: 177 issue: 3–4 year: 2003 ident: 2604_CR20 publication-title: Inf. Sci. doi: 10.1016/S0020-0255(02)00376-6 – volume: 6 start-page: 19 issue: 1 year: 2012 ident: 2604_CR31 publication-title: Signal Image Video Process. doi: 10.1007/s11760-010-0165-9 – volume: 90 start-page: 844 issue: 5 year: 2007 ident: 2604_CR33 publication-title: IEICE Trans. Inf. Syst. doi: 10.1093/ietisy/e90-d.5.844 – volume: 134 start-page: 1 issue: 7 year: 2019 ident: 2604_CR18 publication-title: Eur. Phys. J. Plus doi: 10.1140/epjp/i2019-12704-1 – volume: 120 start-page: 107161 year: 2021 ident: 2604_CR62 publication-title: Appl. Math. Lett. doi: 10.1016/j.aml.2021.107161 – volume: 64 start-page: 1815 issue: 12 year: 2001 ident: 2604_CR6 publication-title: Rep. Prog. Phys. doi: 10.1088/0034-4885/64/12/205 – volume: 29 start-page: 448 issue: 7 year: 2012 ident: 2604_CR45 publication-title: Comput. Aided Geom. Des. doi: 10.1016/j.cagd.2012.03.004 – volume-title: Numerical Optimization year: 2006 ident: 2604_CR67 – volume-title: Applied Regression Analysis year: 1998 ident: 2604_CR12 doi: 10.1002/9781118625590 – volume: 275 start-page: 195 year: 2016 ident: 2604_CR49 publication-title: Appl. Math. Comput. – volume: 54 start-page: 131 issue: 1 year: 2005 ident: 2604_CR39 publication-title: CIRP Ann. doi: 10.1016/S0007-8506(07)60066-3 – volume: 150 start-page: 110487 year: 2021 ident: 2604_CR61 publication-title: Chaos Solitons Fractals doi: 10.1016/j.chaos.2020.110487 – volume: 72 start-page: 095002 issue: 9 year: 2020 ident: 2604_CR63 publication-title: Commun. Theor. Phys. doi: 10.1088/1572-9494/aba23d – volume: 27 start-page: 704 issue: 6 year: 2009 ident: 2604_CR24 publication-title: Image Vis. Comput. doi: 10.1016/j.imavis.2008.07.012 – volume: 57 start-page: 931 issue: 2 year: 2018 ident: 2604_CR25 publication-title: Alex. Eng. J. doi: 10.1016/j.aej.2017.01.004 – volume-title: Curves and Surfaces for Computer Graphics year: 2007 ident: 2604_CR35 – volume: 57 start-page: 1041 issue: 2 year: 2018 ident: 2604_CR13 publication-title: Alex. Eng. J. doi: 10.1016/j.aej.2017.02.016 – volume: 77 start-page: 30331 issue: 23 year: 2018 ident: 2604_CR47 publication-title: Multimedia Tools Appl. doi: 10.1007/s11042-018-6109-z – ident: 2604_CR8 – volume: 150 start-page: 111066 year: 2021 ident: 2604_CR64 publication-title: Chaos Solitons Fractals doi: 10.1016/j.chaos.2021.111066 – volume: 37 start-page: 789 issue: 4 year: 2004 ident: 2604_CR26 publication-title: Pattern Recognit. doi: 10.1016/j.patcog.2003.09.001 – volume: 6 start-page: 34 year: 2012 ident: 2604_CR5 publication-title: Citado – volume: 39 start-page: 439 issue: 6 year: 2007 ident: 2604_CR41 publication-title: Comput.-Aided Des. doi: 10.1016/j.cad.2006.12.006 – volume: 8 start-page: 105 issue: 1 year: 2020 ident: 2604_CR4 publication-title: J. AI Data Min. – ident: 2604_CR42 – ident: 2604_CR53 doi: 10.1007/978-3-662-53090-0_7 – volume: 43 start-page: 947 issue: 3 year: 2019 ident: 2604_CR46 publication-title: Iran. J. Sci. Technol. Trans. A: Sci. doi: 10.1007/s40995-017-0347-1 – ident: 2604_CR19 – volume: 94 start-page: 479 issue: 3 year: 2003 ident: 2604_CR66 publication-title: Numer. Math. doi: 10.1007/s00211-002-0410-4 – volume: 3 start-page: 319 issue: 4 year: 2012 ident: 2604_CR43 publication-title: Int. J. Math. Model. Numer. Optim. – volume: 350 start-page: 664 year: 2019 ident: 2604_CR16 publication-title: Comput. Methods Appl. Mech. Eng. doi: 10.1016/j.cma.2019.03.035 – volume: 58 start-page: 308 issue: 6 year: 2010 ident: 2604_CR23 publication-title: Imaging Sci. J. doi: 10.1179/136821910X12750339175709 – start-page: 455 volume-title: Modeling in Computer Graphics year: 1993 ident: 2604_CR38 doi: 10.1007/978-3-642-78114-8_29 – ident: 2604_CR57 doi: 10.1088/1742-6596/1748/5/052036
SSID	ssj0000491494
Score	2.2837508
Snippet	Curve reconstruction is a significant challenge in computer-aided geometric design, computational atomic and molecular physics, engineering design, virtual...
SourceID	proquest crossref springer
SourceType	Aggregation Database Enrichment Source Index Database Publisher
StartPage	411
SubjectTerms	Algorithms Applied and Technical Physics Approximation Atomic B spline functions CAD Complex Systems Computer aided design Condensed Matter Physics Cultural heritage Curve fitting Data compression Data points Design engineering Error reduction Identification methods Mathematical and Computational Physics Molecular Molecular physics Optical and Plasma Physics Optimization techniques Parameter estimation Parameter identification Physics Physics and Astronomy Production methods Reconstruction Regular Article Scientific visualization Theoretical Video compression Virtual reality Water waves
SummonAdditionalLinks	– databaseName: SpringerLINK Contemporary 1997-Present dbid: RSV link: http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV07T8MwELaggMTCG1EoyAOr1TQPxx4BUTFViJe6WbZjiyLURE0p6r_H5yQtMIAESxbri6yz4_suvvsOoXOqpFKZzIhVzJC4l0aESWmI1Y4eWA4hiPTNJtLBgA2H_PZzqy_Idm-uJP1JXenZBl1TvBTd0oVUNCCQgg5iWDGZr6I15_MYdG24u39a_F5xxNdx_7jO6PoB_9UfLUnmt3tR72762_-Y6A7aqjkmvqg2xS5aMeM9tOFzPXW5jwSEnEvhWJxb7FggHkEakYPpt8nMYCg7wRJP33OSQQOASrwDl8-ycIP5xEMuSQkFvabBjHwS9QF67F8_XN2Qus8C0Y4OTQnlXDGa8UhTZR19CGPlpmyogcCZ9WRPplSFOrGptjzUirM0VMwqmdgoC93jELXG-dgcIZwkIPDHODMu0kkDqsBJgoJ7FKVKct5GtLG20LUIOfTCeBVVgXQgwHqisp5w1hPeemLeRsECWFQ6HL9DOs1yivrDLEXI3ZEDmmasjXrN8i2Hf3nl8R8wJ2gz9NsA6hg7qOVW15yidT2bjsrJmd-1H1ch7AY priority: 102 providerName: Springer Nature
Title	Reconstruction of the initial curve from a two-dimensional shape for the B-spline curve fitting
URI	https://link.springer.com/article/10.1140/epjp/s13360-022-02604-y https://www.proquest.com/docview/2919610128
Volume	137
WOSCitedRecordID	wos000776729400002&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: PRVPQU databaseName: Advanced Technologies & Aerospace Database customDbUrl: eissn: 2190-5444 dateEnd: 20241213 omitProxy: false ssIdentifier: ssj0000491494 issn: 2190-5444 databaseCode: P5Z dateStart: 20110101 isFulltext: true titleUrlDefault: https://search.proquest.com/hightechjournals providerName: ProQuest – providerCode: PRVPQU databaseName: Earth, Atmospheric & Aquatic Science Database customDbUrl: eissn: 2190-5444 dateEnd: 20241213 omitProxy: false ssIdentifier: ssj0000491494 issn: 2190-5444 databaseCode: PCBAR dateStart: 20110101 isFulltext: true titleUrlDefault: https://search.proquest.com/eaasdb providerName: ProQuest – providerCode: PRVPQU databaseName: ProQuest Central customDbUrl: eissn: 2190-5444 dateEnd: 20241213 omitProxy: false ssIdentifier: ssj0000491494 issn: 2190-5444 databaseCode: BENPR dateStart: 20110101 isFulltext: true titleUrlDefault: https://www.proquest.com/central providerName: ProQuest – providerCode: PRVAVX databaseName: SpringerLINK Contemporary 1997-Present customDbUrl: eissn: 2190-5444 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0000491494 issn: 2190-5444 databaseCode: RSV dateStart: 20110101 isFulltext: true titleUrlDefault: https://link.springer.com/search?facet-content-type=%22Journal%22 providerName: Springer Nature
link	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LT9wwEB5RoFIvvNqK5SUferV2N9k49gmxCMRptYK2Qlws27HVrapN2Gyp-PedcRJWcIADl0iWNVbkb2zP2DPfAHwT1lhbmIIHKz0fDfOUS2M8Dw7Ng6DIBTGx2EQ-mcjbWzVtL9zqNqyy2xPjRl2Uju7I-4lCXSEyKnla3XOqGkWvq20JjQ-wQSwJVLphmt093bGg9YsOwKgN60JXou-r31W_Rr9MDDjFsROj1og_Pj-UVpbmi8fReOZcbr_3b3dgq7U22VmjHruw5ud78DFGfbr6M2hyPlcUsqwMDO1BNqOAIhRzfxcPnlECCjNs-a_kBZUCaGg8WP3LVNhZLqLImNeU2us7mVkMp_4CPy4vvp9f8bbiAndoGC25UMpKUajUCRvQkEhGFifIC08utByaocmFTVwWchdU4qySeWJlsCYLaZHg5yusz8u53weWZUT1J5X06PPkA2HpuCQu9zTNrVGqB6Kbcu1aOnKqivFHN6nSA01Y6QYrjVjpiJV-7MHgSbBqGDneFjnqUNLtEq31CqIeDDucV91vDHnw-pCH8CmJ-kXJi0ewjkD6Y9h0D8tZvTiBjfHFZHp9ErUVW9Pz8Rm1rm9-_gc5v_PW
linkProvider	ProQuest
linkToHtml	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1Lb9QwEB6VAoILb8RCAR_gaG3WedkHVJVH1apl1UORKi7GdmyxVbUJm6XV_il-IzNO0hUc6KkHLrlYYynxZ898zsw3AG8Ka6ytTMWDlZ5nkzLl0hjPg8PwICiiICY2myinU3lyoo424NdQC0NplcOZGA_qqnZ0Rz4WCrFCYlRyu_nBqWsU_V0dWmh0sDjwqwukbO27_Y-4vm-F2P10_GGP910FuEPnv-SFUlYWlUpdYQM6S5FZjOl94YkmyomZmLKwwuWhdEEJZ5GUCyuDNXlIK4EPnPcG3MwykdAuOsq_Xt7pYLSNhCPr08iQuox9c9qMW-SBRcIpb54UvDK--tMJriPbv37GRh-3e_9_-zoP4F4fTbOdDv4PYcPPH8HtmNXq2segiVyvJXJZHRjGu2xGCVNo5n4uzj2jAhtm2PKi5hW1OuhkSlj73TQ4WC-iyXveUumyH2xmMV38CXy5lrd7Cpvzeu6fActzkjKUSnrkdGVSWAoHSKs-TUtrlBpBMSyxdr3cOnX9ONNdKXiiCRu6w4ZGbOiIDb0aQXJp2HSKI1ebbA2o0P0R1Oo1JEYwGXC1Hr5iyuf_nvI13Nk7_nyoD_enBy_grojYpkLNLdjERfUv4ZY7X87axau4Qxh8u27Q_QbK40yS
linkToPdf	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1da9swFL106Tb60u6jY-nHpoe9iji2I0uP7ZbQ0hEC-yBvQpIlllEcE3sp-ffVle2E7WGBsRe_iGPElWydY997LsAHppXWucqp09zSdJgllCtlqTOeHjiBEkSFZhPZdMrnczE7gHFXCxOy3btfkk1NA7o0FfWgzF3rbRsNbPmzHFReXrGIYjo6GmOldPMEDlPMpkfR_uX79lOLJ8FeB6Rtdtdf8L-fTTvC-cc_0nD0TE7-06RfwHHLPclVs1lewoEtXsGzkANqqtcgUYruDGXJ0hHPDskC04s8zPxarS3BchSiSP2wpDk2BmhMPUj1Q5V-cLkKkGtaYaGv7TCLkFx9Ct8m468fb2jbf4EaT5NqyoTQnOUiMUw7TyviVPspW2ZRUPOhGqqM6diMXGaciI0WPIs1d1qNXJLH_vIGesWysG-BjEZo_McFt14BZRHTeHiis3uSZFoJ0QfWRV6a1pwce2Tcy6ZwOpIYPdlET_royRA9uelDtAWWjT_HfshFt7SyfWArGQv_KkKvM96HYbeUu-E9tzz7B8x7eD77NJGfb6d353AUhx2BpY4X0PMLbS_hqVnXi2r1LmzmRyhW984
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=Reconstruction+of+the+initial+curve+from+a+two-dimensional+shape+for+the+B-spline+curve+fitting&rft.jtitle=European+physical+journal+plus&rft.au=Jahanshahloo%2C+Almas&rft.au=Ebrahimi%2C+ALireza&rft.date=2022-03-31&rft.pub=Springer+Nature+B.V&rft.eissn=2190-5444&rft.volume=137&rft.issue=3&rft.spage=411&rft_id=info:doi/10.1140%2Fepjp%2Fs13360-022-02604-y
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2190-5444&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2190-5444&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2190-5444&client=summon