Turtle geometry in computer graphics and computer-aided design

LOGO is a programming language incorporating turtle graphics, originally devised for teaching computing to young children in elementary and middle schools. Here, we advocate the use of LOGO to help introduce some of the basic concepts of computer graphics and computer-aided design to undergraduate a...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Computer aided design Jg. 36; H. 14; S. 1471 - 1482
Hauptverfasser: Goldman, Ron, Schaefer, Scott, Ju, Tao
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Ltd 01.12.2004
Schlagworte:
ISSN:0010-4485, 1879-2685
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Abstract LOGO is a programming language incorporating turtle graphics, originally devised for teaching computing to young children in elementary and middle schools. Here, we advocate the use of LOGO to help introduce some of the basic concepts of computer graphics and computer-aided design to undergraduate and graduate students in colleges and universities. We shall show how to motivate affine coordinates and affine transformations, fractal curves and iterated function systems, relaxation methods and subdivision schemes from elementary notions in turtle geometry and turtle programming.
AbstractList LOGO is a programming language incorporating turtle graphics, originally devised for teaching computing to young children in elementary and middle schools. Here, we advocate the use of LOGO to help introduce some of the basic concepts of computer graphics and computer-aided design to undergraduate and graduate students in colleges and universities. We shall show how to motivate affine coordinates and affine transformations, fractal curves and iterated function systems, relaxation methods and subdivision schemes from elementary notions in turtle geometry and turtle programming.
Author Ju, Tao
Goldman, Ron
Schaefer, Scott
Author_xml – sequence: 1
  givenname: Ron
  surname: Goldman
  fullname: Goldman, Ron
  email: rng@cs.rice.edu
– sequence: 2
  givenname: Scott
  surname: Schaefer
  fullname: Schaefer, Scott
  email: sschaefe@rice.edu
– sequence: 3
  givenname: Tao
  surname: Ju
  fullname: Ju, Tao
  email: jutao@cs.rice.edu
BookMark eNqNkU9LAzEQxYMo2FY_gLc9eds6s9nsJgiCiP9A8KLnEJPZmrLdrUlW6Ld3S8WDh9LTMMP7PZj3puy46zti7AJhjoDV1XJujZsXAHzc5wDiiE1Q1iovKimO2QQAIS9LKU7ZNMYlABTI1YTdvA0htZQtqF9RCpvMd5ntV-shUcgWwaw_vY2Z6dzfNTfekcscRb_ozthJY9pI579zxt4f7t_unvKX18fnu9uX3HIpU15JqSynuqltUzUC0ElFSopCOMCGC-FKIUoSvPxQTVNZhVQXDm2hOBokxWfscue7Dv3XQDHplY-W2tZ01A9RF-OrHOEQYSlqQDxEOMZVbx3rndCGPsZAjbY-meT7LgXjW42gtw3opR4b0NsGtqexgZHEf-Q6-JUJm73M9Y6hMc1vT0FH66mz5Hwgm7Tr_R76B1wpnxk
CitedBy_id crossref_primary_10_1017_S0890060408000024
crossref_primary_10_1016_j_envsoft_2008_10_004
crossref_primary_10_1016_j_procs_2023_01_228
crossref_primary_10_1007_s12665_011_1437_6
crossref_primary_10_1007_s40995_016_0129_1
Cites_doi 10.1109/MCG.1981.1673814
10.1109/38.909017
10.1109/MCG.2002.999785
10.1145/504789.504792
10.1016/0167-8396(89)90032-0
10.1109/TPAMI.1980.4766968
ContentType Journal Article
Copyright 2004 Elsevier Ltd
Copyright_xml – notice: 2004 Elsevier Ltd
DBID AAYXX
CITATION
8FD
F28
FR3
7SC
JQ2
L7M
L~C
L~D
DOI 10.1016/j.cad.2003.10.005
DatabaseName CrossRef
Technology Research Database
ANTE: Abstracts in New Technology & Engineering
Engineering Research Database
Computer and Information Systems Abstracts
ProQuest Computer Science Collection
Advanced Technologies Database with Aerospace
Computer and Information Systems Abstracts – Academic
Computer and Information Systems Abstracts Professional
DatabaseTitle CrossRef
Technology Research Database
ANTE: Abstracts in New Technology & Engineering
Engineering Research Database
Computer and Information Systems Abstracts
Computer and Information Systems Abstracts – Academic
Advanced Technologies Database with Aerospace
ProQuest Computer Science Collection
Computer and Information Systems Abstracts Professional
DatabaseTitleList Technology Research Database
Computer and Information Systems Abstracts
Technology Research Database

DeliveryMethod fulltext_linktorsrc
Discipline Engineering
EISSN 1879-2685
EndPage 1482
ExternalDocumentID 10_1016_j_cad_2003_10_005
S0010448504000521
GroupedDBID --K
--M
-~X
.DC
.~1
0R~
1B1
1~.
1~5
29F
4.4
457
4G.
5GY
5VS
6TJ
7-5
71M
8P~
9JN
AABNK
AACTN
AAEDT
AAEDW
AAIAV
AAIKC
AAIKJ
AAKOC
AALRI
AAMNW
AAOAW
AAQFI
AAQXK
AAXUO
AAYFN
ABAOU
ABBOA
ABEFU
ABFNM
ABFRF
ABMAC
ABXDB
ABYKQ
ACAZW
ACBEA
ACDAQ
ACGFO
ACGFS
ACIWK
ACKIV
ACNNM
ACRLP
ACZNC
ADBBV
ADEZE
ADGUI
ADJOM
ADMUD
ADTZH
AEBSH
AECPX
AEFWE
AEKER
AENEX
AFFNX
AFKWA
AFTJW
AGHFR
AGUBO
AGYEJ
AHHHB
AHJVU
AHZHX
AIALX
AIEXJ
AIGVJ
AIKHN
AITUG
AJBFU
AJOXV
ALMA_UNASSIGNED_HOLDINGS
AMFUW
AMRAJ
AOUOD
ARUGR
ASPBG
AVWKF
AXJTR
AZFZN
BJAXD
BKOJK
BLXMC
CS3
DU5
EBS
EFJIC
EFLBG
EJD
EO8
EO9
EP2
EP3
F5P
FDB
FEDTE
FGOYB
FIRID
FNPLU
FYGXN
G-2
G-Q
G8K
GBLVA
GBOLZ
HLZ
HVGLF
HZ~
IHE
J1W
JJJVA
K-O
KOM
LG9
LY7
M41
MHUIS
MO0
N9A
O-L
O9-
OAUVE
OZT
P-8
P-9
P2P
PC.
PQQKQ
Q38
R2-
RIG
RNS
ROL
RPZ
RXW
SBC
SDF
SDG
SDP
SES
SET
SEW
SPC
SPCBC
SST
SSV
SSW
SSZ
T5K
TAE
TN5
TWZ
VOH
WUQ
XFK
XPP
ZMT
~G-
9DU
AATTM
AAXKI
AAYWO
AAYXX
ABDPE
ABJNI
ABWVN
ACLOT
ACRPL
ACVFH
ADCNI
ADNMO
AEIPS
AEUPX
AFJKZ
AFPUW
AGQPQ
AIGII
AIIUN
AKBMS
AKRWK
AKYEP
ANKPU
APXCP
CITATION
EFKBS
~HD
8FD
F28
FR3
7SC
JQ2
L7M
L~C
L~D
ID FETCH-LOGICAL-c388t-6889c3e7f7cf6f501d89e98525d01f355d4554e534b9ff6c91e72d1c2931a1e93
ISICitedReferencesCount 13
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000224906800006&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 0010-4485
IngestDate Wed Oct 01 14:01:41 EDT 2025
Sun Sep 28 07:10:18 EDT 2025
Sat Sep 27 22:56:13 EDT 2025
Sat Nov 29 05:38:45 EST 2025
Tue Nov 18 21:22:48 EST 2025
Fri Feb 23 02:26:57 EST 2024
IsPeerReviewed true
IsScholarly true
Issue 14
Keywords Iterated function system
Turtle geometry
Fractal
Bezier curve
Affine transformation
Language English
License https://www.elsevier.com/tdm/userlicense/1.0
LinkModel OpenURL
MergedId FETCHMERGED-LOGICAL-c388t-6889c3e7f7cf6f501d89e98525d01f355d4554e534b9ff6c91e72d1c2931a1e93
Notes ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
PQID 28444879
PQPubID 23500
PageCount 12
ParticipantIDs proquest_miscellaneous_28793109
proquest_miscellaneous_28457011
proquest_miscellaneous_28444879
crossref_citationtrail_10_1016_j_cad_2003_10_005
crossref_primary_10_1016_j_cad_2003_10_005
elsevier_sciencedirect_doi_10_1016_j_cad_2003_10_005
PublicationCentury 2000
PublicationDate 2004-12-01
PublicationDateYYYYMMDD 2004-12-01
PublicationDate_xml – month: 12
  year: 2004
  text: 2004-12-01
  day: 01
PublicationDecade 2000
PublicationTitle Computer aided design
PublicationYear 2004
Publisher Elsevier Ltd
Publisher_xml – name: Elsevier Ltd
References Ju T, Schaefer S, Goldman R. Recursive turtle programs and iterated affine transformations, Computers and Graphics, submitted for publication.
Ramshaw (BIB17) 1989; 6
Warren J. Private communication; 1993.
Goldman (BIB6) 2001; 21
Murray, Li, Sastry (BIB14) 1994
Dorst, Mann (BIB5) 2002; 22
Riesenfeld (BIB18) 1981; 1
de Casteljau (BIB4) 1985
Harvey (BIB10) (1985–1987); vols. 1–3
Abelson, diSessa (BIB1) 1986
Goldman (BIB8) 2002; 21
Sillion, Puech (BIB20) 1994
Hoffmann (BIB11) 1989
Lane, Riesenfeld (BIB13) 1980; 2
Goldman (BIB7) 2002
Goldman (BIB9) 2003
Sederberg, Gao, Wang, Mu (BIB19) 1993
Prusinkiewicz (BIB16) 1986
Blinn (BIB3) 2002
Barnsley (BIB2) 1993
Papert (BIB15) 1980
Murray (10.1016/j.cad.2003.10.005_BIB14) 1994
Papert (10.1016/j.cad.2003.10.005_BIB15) 1980
Sederberg (10.1016/j.cad.2003.10.005_BIB19) 1993
Goldman (10.1016/j.cad.2003.10.005_BIB8) 2002; 21
Ramshaw (10.1016/j.cad.2003.10.005_BIB17) 1989; 6
Barnsley (10.1016/j.cad.2003.10.005_BIB2) 1993
de Casteljau (10.1016/j.cad.2003.10.005_BIB4) 1985
Hoffmann (10.1016/j.cad.2003.10.005_BIB11) 1989
Dorst (10.1016/j.cad.2003.10.005_BIB5) 2002; 22
Prusinkiewicz (10.1016/j.cad.2003.10.005_BIB16) 1986
Sillion (10.1016/j.cad.2003.10.005_BIB20) 1994
Abelson (10.1016/j.cad.2003.10.005_BIB1) 1986
Goldman (10.1016/j.cad.2003.10.005_BIB9) 2003
Lane (10.1016/j.cad.2003.10.005_BIB13) 1980; 2
10.1016/j.cad.2003.10.005_BIB21
Harvey (10.1016/j.cad.2003.10.005_BIB10) 1985; vols. 1–3
Goldman (10.1016/j.cad.2003.10.005_BIB6) 2001; 21
Goldman (10.1016/j.cad.2003.10.005_BIB7) 2002
10.1016/j.cad.2003.10.005_BIB12
Riesenfeld (10.1016/j.cad.2003.10.005_BIB18) 1981; 1
Blinn (10.1016/j.cad.2003.10.005_BIB3) 2002
References_xml – volume: 22
  start-page: 24
  year: 2002
  end-page: 31
  ident: BIB5
  article-title: Geometric algebra: a computational framework for geometric applications. Parts I and II
  publication-title: IEEE Comput Graphics Applic
– year: 2002
  ident: BIB7
  publication-title: Pyramid algorithms: a dynamic programming approach to curves and surfaces for geometric modeling
– volume: 2
  start-page: 35
  year: 1980
  end-page: 46
  ident: BIB13
  article-title: A theoretical development for the computer generation and display of piecewise polynomial surfaces
  publication-title: IEEE Trans Pattern Anal Mach Intell
– volume: 21
  start-page: 70
  year: 2001
  end-page: 78
  ident: BIB6
  article-title: Baseball arithmetic and the laws of pseudoperspective
  publication-title: IEEE Comput Graphics Applic
– year: 1980
  ident: BIB15
  publication-title: Mindstorms: children, computers and powerful ideas
– reference: Ju T, Schaefer S, Goldman R. Recursive turtle programs and iterated affine transformations, Computers and Graphics, submitted for publication.
– volume: 6
  start-page: 323
  year: 1989
  end-page: 358
  ident: BIB17
  article-title: Blossoms are polar forms
  publication-title: Comput-Aided Geometr Des
– start-page: 15
  year: 1993
  end-page: 18
  ident: BIB19
  article-title: An intrinsic solution to the vertex path problem
  publication-title: Comput Graphics (Proc Siggraph'93)
– year: 1994
  ident: BIB14
  publication-title: A mathematical introduction to robotic manipulation
– year: 1986
  ident: BIB16
  article-title: Graphical applications of L-systems
  publication-title: Proceedings of Graphical Interface 86 and Vision Interface 86
– reference: Warren J. Private communication; 1993.
– year: 1985
  ident: BIB4
  publication-title: Formes a Poles
– year: 1994
  ident: BIB20
  publication-title: Radiosity and global illumination
– year: 2003
  ident: BIB9
  article-title: Computer graphics in its fifth decade: ferment at the foundations, (Invited Paper)
  publication-title: Pacific Graphics 2003
– volume: 21
  start-page: 1
  year: 2002
  end-page: 35
  ident: BIB8
  article-title: On the algebraic and geometric foundations of computer graphics
  publication-title: Trans Graphics
– year: 1993
  ident: BIB2
  publication-title: Fractals everywhere
– year: 1989
  ident: BIB11
  publication-title: Geometric and solid modeling: an introduction
– year: 1986
  ident: BIB1
  publication-title: Turtle geometry: the computer as a medium for exploring mathematics
– year: 2002
  ident: BIB3
  article-title: Using tensor diagrams to represent and solve geometric problems
  publication-title: Siggraph 2002, Course 25
– volume: 1
  start-page: 50
  year: 1981
  end-page: 55
  ident: BIB18
  article-title: Homogeneous coordinates and the projective plane in computer graphics
  publication-title: IEEE Comput Graphics Applic
– volume: vols. 1–3
  year: (1985–1987)
  ident: BIB10
  publication-title: Computer Science LOGO Style
– volume: vols. 1–3
  year: 1985
  ident: 10.1016/j.cad.2003.10.005_BIB10
– year: 2003
  ident: 10.1016/j.cad.2003.10.005_BIB9
  article-title: Computer graphics in its fifth decade: ferment at the foundations, (Invited Paper)
– year: 1986
  ident: 10.1016/j.cad.2003.10.005_BIB16
  article-title: Graphical applications of L-systems
– ident: 10.1016/j.cad.2003.10.005_BIB12
– year: 1994
  ident: 10.1016/j.cad.2003.10.005_BIB14
– year: 1985
  ident: 10.1016/j.cad.2003.10.005_BIB4
– volume: 1
  start-page: 50
  year: 1981
  ident: 10.1016/j.cad.2003.10.005_BIB18
  article-title: Homogeneous coordinates and the projective plane in computer graphics
  publication-title: IEEE Comput Graphics Applic
  doi: 10.1109/MCG.1981.1673814
– year: 2002
  ident: 10.1016/j.cad.2003.10.005_BIB7
– year: 1980
  ident: 10.1016/j.cad.2003.10.005_BIB15
– year: 1986
  ident: 10.1016/j.cad.2003.10.005_BIB1
– volume: 21
  start-page: 70
  year: 2001
  ident: 10.1016/j.cad.2003.10.005_BIB6
  article-title: Baseball arithmetic and the laws of pseudoperspective
  publication-title: IEEE Comput Graphics Applic
  doi: 10.1109/38.909017
– year: 2002
  ident: 10.1016/j.cad.2003.10.005_BIB3
  article-title: Using tensor diagrams to represent and solve geometric problems
– year: 1994
  ident: 10.1016/j.cad.2003.10.005_BIB20
– volume: 22
  start-page: 24
  issue: 3
  year: 2002
  ident: 10.1016/j.cad.2003.10.005_BIB5
  article-title: Geometric algebra: a computational framework for geometric applications. Parts I and II
  publication-title: IEEE Comput Graphics Applic
  doi: 10.1109/MCG.2002.999785
– volume: 21
  start-page: 1
  year: 2002
  ident: 10.1016/j.cad.2003.10.005_BIB8
  article-title: On the algebraic and geometric foundations of computer graphics
  publication-title: Trans Graphics
  doi: 10.1145/504789.504792
– volume: 6
  start-page: 323
  year: 1989
  ident: 10.1016/j.cad.2003.10.005_BIB17
  article-title: Blossoms are polar forms
  publication-title: Comput-Aided Geometr Des
  doi: 10.1016/0167-8396(89)90032-0
– start-page: 15
  year: 1993
  ident: 10.1016/j.cad.2003.10.005_BIB19
  article-title: An intrinsic solution to the vertex path problem
  publication-title: Comput Graphics (Proc Siggraph'93)
– ident: 10.1016/j.cad.2003.10.005_BIB21
– year: 1989
  ident: 10.1016/j.cad.2003.10.005_BIB11
– volume: 2
  start-page: 35
  year: 1980
  ident: 10.1016/j.cad.2003.10.005_BIB13
  article-title: A theoretical development for the computer generation and display of piecewise polynomial surfaces
  publication-title: IEEE Trans Pattern Anal Mach Intell
  doi: 10.1109/TPAMI.1980.4766968
– year: 1993
  ident: 10.1016/j.cad.2003.10.005_BIB2
SSID ssj0002139
Score 1.848419
Snippet LOGO is a programming language incorporating turtle graphics, originally devised for teaching computing to young children in elementary and middle schools....
SourceID proquest
crossref
elsevier
SourceType Aggregation Database
Enrichment Source
Index Database
Publisher
StartPage 1471
SubjectTerms Affine transformation
Bezier curve
Fractal
Iterated function system
Turtle geometry
Title Turtle geometry in computer graphics and computer-aided design
URI https://dx.doi.org/10.1016/j.cad.2003.10.005
https://www.proquest.com/docview/28444879
https://www.proquest.com/docview/28457011
https://www.proquest.com/docview/28793109
Volume 36
WOSCitedRecordID wos000224906800006&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: PRVESC
  databaseName: Elsevier SD Freedom Collection Journals 2021
  customDbUrl:
  eissn: 1879-2685
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0002139
  issn: 0010-4485
  databaseCode: AIEXJ
  dateStart: 19950101
  isFulltext: true
  titleUrlDefault: https://www.sciencedirect.com
  providerName: Elsevier
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV3LbhMxFLUgZQELxFP0AcwCsSAaNB7bY3uDVFWpoKoCEqmUneV47KpVmYQ8qn5-r8d2EgIEWLCZRJYniXyce4_tO-cg9MaaSlqg_bkgDhYolupcaFzlTpecjUpKtBat2QTv98VwKL9El75ZayfAm0bc3MjJf4Ua2gBs_-jsP8C9_FBogPcAOlwBdrj-HfCLKbx0z-34m51P28f6TLRu6Lby1EmXObXmXiWy7tarWo6kXJBu-6lDK6h_Vcfd0-Vh0Vdfgu82rLxOFqta7LS9QNdKNWLIhEANYLL1kBk0S9LUoGsBENPgqBKTqVcZ_WWgDnsGl7AID3Kt79sSO7bKSukkvv9ZHZ-dnqpBbzh4O_mee78wf64ezVPuoh2YVFJ00M7hp97wZJmFS0zC0if-_HSi3db2bXzr7zjJRnZuKcfgEXoY1wrZYcD4MbpjmyfowZqC5FP0IaCdJbSziyZLuGYJ7QzQzn5EOwtgPkNnx73B0cc8WmLkhggxzyshpCGWO25c5ViBayGtFKxkdYEdcMeaAj-0jNCRdK4yElte1tgAqcMaW0meo04zbuwLlAG1lg4WpMDnNSUVMD1KnalZMdKMiYrvoiINijJRL97bllypVBh4qWAcvY8p8U0wjrvo3fKWSRBL2daZppFWke0FFqdgjmy77XVCRUEk9MdburHjxUwB0QKgudzag3FIaNt6QL7Chdz7Y499dH_1dzlAnfl0YV-ie-Z6fjGbvoqz8Rbr85NK
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=Turtle+geometry+in+computer+graphics+and+computer-aided+design&rft.jtitle=Computer+aided+design&rft.au=Goldman%2C+R&rft.au=Schaefer%2C+S&rft.au=Ju%2C+T&rft.date=2004-12-01&rft.issn=0010-4485&rft.volume=36&rft.issue=14&rft.spage=1471&rft.epage=1482&rft_id=info:doi/10.1016%2Fj.cad.2003.10.005&rft.externalDBID=NO_FULL_TEXT
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0010-4485&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0010-4485&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0010-4485&client=summon