Computer Graphics and Geometric Ornamental Design - Versionsgeschichte

Gbachelier am 25. Januar 2015 um 21:31 Uhr

2015-01-25T21:31:35Z

Gbachelier: /* Used References */

2014-12-03T18:08:30Z

‎Used References

Gbachelier: /* Used References */

2014-12-03T17:52:32Z

‎Used References

Gbachelier: Die Seite wurde neu angelegt: „ == Reference == Craig S. Kaplan: Computer Graphics and Geometric Ornamental Design. Ph.D. Thesis, University of Washington, 2002. == DOI == == Abstract ==…“

2014-12-03T17:52:03Z

Die Seite wurde neu angelegt: „ == Reference == Craig S. Kaplan: Computer Graphics and Geometric Ornamental Design. Ph.D. Thesis, University of Washington, 2002. == DOI == == Abstract ==…“

Neue Seite

== Reference ==
Craig S. Kaplan: Computer Graphics and Geometric Ornamental Design. Ph.D. Thesis, University of Washington, 2002.

== DOI ==

== Abstract ==
Throughout history, geometric patterns have formed an important part of art and ornamental design.
Today we have unprecedented ability to understand ornamental styles of the past, to recreate tradi-
tional designs, and to innovate with new interpretations of old styles and with new styles altogether.
The power to further the study and practice of ornament stems from three sources. We have new
mathematical tools: a modern conception of geometry that enables us to describe with precision
what designers of the past could only hint at. We have new algorithmic tools: computers and the
abstract mathematical processing they enable allow us to perform calculations that were intractable
in previous generations. Finally, we have technological tools: manufacturing devices that can turn a
synthetic description provided by a computer into a real-world artifact. Taken together, these three
sets of tools provide new opportunities for the application of computers to the analysis and creation
of ornament.
In this dissertation, I present my research in the area of computer-generated geometric art and
ornament. I focus on two projects in particular. First I develop a collection of tools and methods
for producing traditional Islamic star patterns. Then I examine the tesselations of M. C. Escher,
developing an “Escherization” algorithm that can derive novel Escher-like tesselations of the plane
from arbitrary user-supplied shapes. Throughout, I show how modern mathematics, algorithms, and
technology can be applied to the study of these ornamental styles.

== Extended Abstract ==

== Bibtex ==

== Used References ==
[1] Jan Abas. A hyperbolic mural. http://www.bangor.ac.uk/~mas009/ppic7.html.

[2] Syed Jan Abas and Amer Shaker Salman. Symmetries of Islamic Geometrical Patterns. World
Scientific, 1995.

[3] Steve Abbott. Steve Abbott’s computer drawn Celtic knotwork. http://www.abbott.demon.co.uk/knots.html.

[4] Maneesh Agrawala and Chris Stolte. Rendering effective route maps: Improving usability
through generalization. Proceedings of SIGGRAPH 2001, pages 241–250, 2001.

[5] Nina Amenta and Mark Phillips. Kali. http://www.geom.umn.edu/java/Kali/.

[6] E. M. Arkin, L. P. Chew, D. P. Huttenlocher, K. Kedem, and J. S. B. Mitchell. An efficiently
computable metric for comparing polygonal shapes. IEEE Transactions on Pattern Analysis
and Machine Intelligence, 13:209–216, 1991.

[7] George Bain. The Methods of Construction of Celtic Art. Dover, 1973.

[8] Thaddeus Beier and Shawn Neely. Feature-based image metamorphosis. Proceedings of
SIGGRAPH’92, pages 35–42, 1992.

[9] John Berglund. Anisohedral tilings page. http://www.angelfire.com/mn3/anisohedral/

[10] John Berglund. Is there a k-anisohedral tile for k ≥ 5? American Mathematical Monthly,
100:585–588, 1993.

[11] Jinny Beyer. Designing Tesselations: The Secrets of Interlocking Patterns. Contemporary
Books, 1999.
[12] Jay Bonner. Geodazzlers. http://www.dstoys.com/GD.html.

[13] Jay Francis Bonner. Islamic Geometric Patterns: Their Historical Development and Tradi-
tional Methods of Derivation. Unpublished, 2000.

[14] Roberto Bonola. Non-Euclidean Geometry. Dover Publications, 1955.201

[15] F. H. Bool, J. R. Kist, J. L. Locher, and F. Wierda. M. C. Escher: His Life and Complete
Graphic Work. Harry N. Abrams, Inc., 1992.

[16] J. Bourgoin. Arabic Geometrical Pattern and Design. Dover Publications, 1973.

[17] Cameron Browne. Font decoration by automatic mesh fitting. In R.D. Hersch, J. Andr, and
H. Brown, editors, Electronic Publishing, Artistic Imaging, and Digital Typography, pages
23–43. Springer Verlag, 1998.

[18] Paul Burchard, Daeron Meyer, and Eugenio Durand. Quasitiler. http://www.geom.umn.edu/apps/quasitiler/.

[19] Jean-Marc Cast ́era. Arabesques: Decorative Art in Morocco. ACR Edition, 1999.

[20] Jean-Marc Cast ́era. Zellijs, muqarnas and quasicrystals. In Nathaniel Friedman and Javiar
Barrallo, editors, ISAMA 99 Proceedings, pages 99–104, 1999.

[21] William W. Chow. Automatic generation of interlocking shapes. Computer Graphics and
Image Processing, 9:333–353, 1979.

[22] Archibald Christie. Traditional Methods of Pattern Designing. Oxford University Press,
1929.

[23] Alain Connes. Noncommutative Geometry. Academic Press, San Diego, 1994.

[24] H. S. M. Coxeter. Coloured symmetry. In H. S. M. Coxeter et al., editor, M.C. Escher: Art
and Science, pages 15–33. Elsevier Science Publishers B.V., 1986.

[25] H. S. M. Coxeter. Non-Euclidean Geometry. Mathematical Association of America, sixth
edition, 1998.

[26] H. S. M. Coxeter and W. O. J. Moser. Generators and Relations for Discrete Groups.
Springer-Verlag, 1980.

[27] Keith Critchlow. Islamic Patterns: An Analytical and Cosmological Approach. Thames and
Hudson, 1976.

[28] Hallard T. Croft, Kenneth J. Falconer, and Richard K. Guy. Unsolved Problems in Geometry.
Springer-Verlag, 1991.

[29] Peter R. Cromwell. Celtic knotwork: Mathematical art. The Mathematical Intelligencer,
15(1):36–47, 1993.202

[30] L. Danzer, B. Gr ̈unbaum, and G. C. Shephard. Can all tiles of a tiling have five-fold symme-
try? American Mathematical Monthly, 89:568–585, 1982.

[31] Prisse d’Avennes. Arabic Art. L’Aventurine, 2001.

[32] Doug DeCarlo and Anthony Santella. Stylization and abstraction of photographs. Proceed-
ings of SIGGRAPH 2002, pages 769–776, 2002.

[33] Olaf Delgado, Daniel Huson, and Elizaveta Zamorzaeva. The classification of 2-isohedral
tilings of the plane. Geometricae Dedicata, 42:43–117, 1992.

[34] Olaf Delgado-Friedrichs. Data structures and algorithms for tilings. To be published in
Theoretical Computer Science.

[35] Tony DeRose, Michael Kass, and Tien Truong. Subdivision surfaces in character anima-
tion. In Proceedings of the 25th annual conference on Computer graphics and interactive
techniques (SIGGRAPH’98), pages 85–94. ACM Press, 1998.

[36] A.K. Dewdney. The Tinkertoy Computer and Other Machinations, pages 222–230. W. H.
Freeman, 1993.

[37] Robert Dixon. Two conformal mappings. In Michele Emmer, editor, The Visual Mind: Art
and Mathematics, pages 45–48. MIT Press, 1993.

[38] Andreas W. M. Dress. The 37 combinatorial types of regular “Heaven and Hell” patterns in
the euclidean plane. In H. S. M. Coxeter et al., editor, M.C. Escher: Art and Science, pages
35–45. Elsevier Science Publishers B.V., 1986.

[39] Douglas Dunham. Hyperbolic symmetry. Computers and Mathematics with Applications,
12B(1/2):139–153, 1986.

[40] Douglas Dunham. Artistic patterns in hyperbolic geometry. In Reza Sarhangi, editor, Bridges
1999 Proceedings, pages 139–149, 1999.

[41] Douglas Dunham. Hyperbolic Islamic patterns — a beginning. In Reza Sarhangi, editor,
Bridges 2001 Proceedings, pages 247–254, 2001.

[42] Douglas Dunham, John Lindgren, and David Witte. Creating repeating hyperbolic patterns.
Computer Graphics (Proc. SIGGRAPH), pages 215–223, 1981.

[43] Douglas J. Dunham. Creating hyperbolic escher patterns. In H. S. M. Coxeter et al., editor,
M.C. Escher: Art and Science, pages 241–247. Elsevier Science Publishers B.V., 1986.203

[44] David S. Ebert, F. Kenton Musgrave, Darwyn Peachey, Ken Perlin, and Steven Worley. Tex-
turing and Modeling. AP Professional, 1998.

[45] David Eppstein. The geometry junkyard: Penrose tiling. http://www.ics.uci.edu/~eppstein/junkyard/penrose.html.

[46] David B. A. Epstein, J .W. Cannon, D. F. Holt, S. V. F. Levy, M. S. Paterson, and W. P.
Thurston. Word Processing in Groups. Jones and Bartlett, 1992.

[47] Bruno Ernst. The Magic Mirror of M. C. Escher. Ballantine Books, New York, 1976.

[48] George A. Escher. M.C. escher at work. In H. S. M. Coxeter et al., editor, M.C. Escher: Art
and Science, pages 1–8. Elsevier Science Publishers B.V., 1986.

[49] M. C. Escher. Escher on Escher: Exploring the Infinite. Henry N. Abrams, Inc., 1989.
Translated by Karin Ford.

[50] Richard L. Faber. Foundations of Eucliedean And Non-Euclidean Geometry. Marcel Dekker,
Inc., 1993.

[51] Michael Field and Martin Golubitsky. Symmetry in Chaos. Oxford University Press, 1992.

[52] Franc ̧ois Dispot. Arabeske home page. http://www.wozzeck.net/arabeske/index.html.

[53] The gimp. http://www.gimp.org/.

[54] Andrew Glassner. Andrew Glassner’s notebook: Aperiodic tiling. IEEE Computer Graphics
& Applications, 18(3):83–90, may–jun 1998. ISSN 0272-1716.

[55] Andrew Glassner. Andrew Glassner’s notebook: Penrose tiling. IEEE Computer Graphics &
Applications, 18(4), jul–aug 1998. ISSN 0272-1716.

[56] Andrew Glassner. Andrew Glassner’s notebook: Celtic knots, part II. IEEE Computer Graph-
ics & Applications, 19(6):82–86, nov–dec 1999. ISSN 0272-1716.

[57] Andrew Glassner. Andrew Glassner’s notebook: Celtic knotwork, part I. IEEE Computer
Graphics & Applications, 19(5):78–84, sep–oct 1999. ISSN 0272-1716.

[58] Andrew Glassner. Andrew Glassner’s notebook: Celtic knots, part III. IEEE Computer
Graphics & Applications, 20(1):70–75, jan–feb 2000. ISSN 0272-1716.

[59] Solomon W. Golomb. Polyominoes: Puzzles, Patterns, Problems and Packings. Princeton
University Press, second edition, 1994.204

[60] E. H. Gombrich. The Sense of Order: A Study in the Psychology of Decorative Art. Phaidon
Press Limited, second edition, 1998.

[61] Chaim Goodman-Strauss. A small set of aperiodic tiles. European Journal of Combinatorics,
20:375–384, 1999.

[62] Marvin J. Greenberg. Euclidean and Non-Euclidean Geometries: Development and History.
W. H. Freeman and Company, third edition, 1993.

[63] Bathsheba Grossman. Bathsheba Grossman – sculpting geometry. http://www. bathsheba.com/.

[64] Branko Gr ̈unbaum. The emperor’s new clothes: Full regalia, G string, or nothing?
Mathematical Intelligencer, 6(4):47–53, 1984.

[65] Branko Gr ̈unbaum. Periodic ornamentation of the fabric plane: Lessons from Peruvian fab-
rics. Symmetry, 1(1):45–68, 1990.

[66] Branko Gr ̈unbaum. Levels of orderliness: Global and local symmetry. In I. Hargittai and
T. C. Laurent, editors, Symmetry 2000, pages 51–61. Portland Press, London, 2002.

[67] Branko Gr ̈unbaum and G. C. Shephard. Spherical tilings with transitivity properties. In Chan-
dler Davis, Branko Gr ̈unbaum, and F. A. Sherk, editors, The Geometric Vein: The Coxeter
Festschrift, pages 65–94. Springer-Verlag, New York, 1982.

[68] Branko Gr ̈unbaum and G. C. Shephard. Tilings and Patterns. W. H. Freeman, 1987.

[69] Branko Gr ̈unbaum and G. C. Shephard. Interlace patterns in Islamic and Moorish art.
Leonardo, 25:331–339, 1992.

[70] E. H. Hankin. The Drawing of Geometric Patterns in Saracenic Art, volume 15 of Memoirs
of the Archaeological Society of India. Government of India, 1925.

[71] E. Hanbury Hankin. Examples of methods of drawing geometrical arabesque patterns. The
Mathematical Gazette, pages 371–373, May 1925.

[72] E. Hanbury Hankin. Some difficult Saracenic designs II. The Mathematical Gazette, pages
165–168, July 1934.

[73] E. Hanbury Hankin. Some difficult Saracenic designs III. The Mathematical Gazette, pages
318–319, December 1936.

[74] Istv ́an Hargittai and Magdolna Hargittai. Symmetry through the Eyes of a Chemist. Plenum
Press, New York, second edition, 1995.205

[75] George W. Hart. Conway notation for polyhedra. http://www.georgehart.com/
virtual-polyhedra/conway_notation.html.

[76] George W. Hart. Geometric sculpture. http://www.georgehart.com/sculpture/sculpture.html.

[77] George W. Hart. Uniform polyhedra. http://www.georgehart.com/virtual-polyhedra/uniform-info.html.

[78] Barbara Hausmann, Britta Slopianka, and Hans-Peter Seidel. Exploring plane hyperbolic ge-
ometry. In Hans-Christian Hege and Konrad Polthier, editors, Visualization and Mathematics,
pages 21–36. Springer, 1997.

[79] H. Heesch. Aufbau der ebene aus kongruenten bereichen. Nachrichten von der Gesellschaft
der Wissenschaften zu G ̈ottingen, pages 115–117, 1935. John Berglund provides an
online English translation at http://www.angelfire.com/mn3/anisohedral/heesch35.html.

[80] H. Heesch and O. Kienzle. Flachenschluss. Springer–Verlag, 1963.

[81] Richard E. Hodel. An Introduction to Mathematical Logic. PWS Publishing Company, 1995.

[82] Paul Hoffman. The Man Who Loved Only Numbers. Hyperion, New York, 1998.

[83] Douglas Hofstadter. Metamagical Themas: Questing for the Essence of Mind and Pattern.
Bantam Books, 1986.

[84] Alan Holden. Shapes, Space, and Symmetry. Dover Publications, Inc., 1991.

[85] Edmund S. Howe. Effects of partial symmetry, exposure time, and backward masking on
judged goodness and reproduction of visual patterns. Quarterly Journal of Experimental
Psychology, 32:27–55, 1980.

[86] Daniel H. Huson. The generation and classification of tile-k-transitive tilings of the euclidean
plane, the sphere, and the hyperbolic plane. Geometriae Dedicata, 47:269–296, 1993.

[87] Pedagoguery Software Inc. Tess. http://www.peda.com/tess/Welcome.html.

[88] Washington Irving. The Alhambra. Macmillan and co., 1931.

[89] Drew Ivans. The origin and meaning of Celtic knotwork. http://www.craytech.com/drew/knotwork/knotwork-meaning.html.206

[90] Robert Jensen and Patricia Conway. Ornamentalism: the New Decorativeness in Artchitec-
ture & Design. Clarkson N. Potter, Inc., 1982.

[91] Owen Jones. The Grammar of Ornament. Studio Editions, 1986.

[92] Craig S. Kaplan. isohedral.ih. http://www.cs.washington.edu/homes/csk/tile/escherization.html.

[93] Craig S. Kaplan. Computer generated islamic star patterns. In Reza Sarhangi, editor, Bridges
2000 Proceedings, 2000.

[94] Craig S. Kaplan. Computer generated islamic star patterns. Visual Mathematics, 2(3), 2000.
http://members.tripod.com/vismath4/kaplan/index.html.

[95] Craig S. Kaplan and George W. Hart. Symmetrohedra: Polyhedra from symmetric placement
of regular polygons. In Reza Sarhangi, editor, Bridges 2001 Proceedings, 2001.

[96] Craig S. Kaplan and David H. Salesin. Escherization. In Proceedings of the 27th annual
conference on Computer graphics and interactive techniques (SIGGRAPH 2000), pages 499–
510. ACM Press/Addison-Wesley Publishing Co., 2000.

[97] David C. Kay. College Geometry. Holt, Rinehart and Winston, Inc., 1969.

[98] Haresh Lalvani. Pattern regeneration: A focus on Islamic jalis and mosaics. In Jan Pieper and
George Michell, editors, The Impulse to Adorn, pages 123–136. Marg Publications, 1982.

[99] A.J. Lee. Islamic star patterns. Muqarnas, 4:182–197, 1995.

[100] Raph Levien. libart. http://www.levien.com/libart/.

[101] Silvio Levy. Automatic generation of hyperbolic tilings. In Michele Emmer, editor, The
Visual Mind: Art and Mathematics, pages 165–170. MIT Press, 1993.

[102] Michael Leyton. A Generative Theory of Shape, volume 2145 of Lecture Notes in Computer
Science. Springer, 2001.

[103] Ming Li and Paul Vit ́anyi. An Introduction to Kolmogorov Complexity and its Applications.
Graduate texts in Computer Science. Springer-Verlag, Inc., New York, second edition, 1997.

[104] Stanley B. Lippman and Jos ́ee Lajoie. C++ Primer. Addison-Wesley, third edition, 1998.

[105] J. L. Locher. The Magic of M. C. Escher. Harry N. Abrams, Inc., 2000. Designed by Erik
Th ́e.207

[106] P. Locher and C. Nodine. The perceptual value of symmetry. Computers and Mathematics
With Applications, 17(4–6):475–484, 1989.

[107] Z. Luˇci ́c and E. Moln ́ar. Fundamental domains for planar discontinuous groups and uniform
tilings. Geometriae Dedicata, 40:125–143, 1991.

[108] Wilhelm Magnus, Abraham Karrass, and Donald Solitar. Combinatorial group theory: pre-
sentations of groups in terms of generators and relations. Dover Publications, 1976.

[109] George E. Martin. The Foundations of Geometry and the Non-Euclidean Plane. Intext Edu-
cational Publishers, 1975.

[110] Scott McCloud. Understanding Comics. HarperCollins, 1993.

[111] Christian Mercat. Celtic knotwork, the ultimate tutorial. http://www.entrelacs.
net/en.index.html.

[112] Kevin Mitchell. Semi-regular tilings of the plane. mitchell/tilings/Part1.html. http://people.hws.edu/

[113] Anders Pape Møller and John P. Swaddle. The biological importance of imperfect symmetry.
In Asymmetry, Developmental Stability and Evolution, chapter W1. Oxford University Press,
1997. Available online from http://www.oup.co.uk/isbn/0-19-854894-X.

[114] E. N. Mortenson and W. A. Barrett. Intelligent scissors for image composition. Proceedings
of SIGGRAPH 1995, pages 191–198, 1995.

[115] Joseph Myers. Polyomino, polyhex, and polyiamond tiling. http://www.srcf.ucam.org/~jsm28/tiling/.

[116] G ̈ulru Necipoˇglu. The Topkapı Scroll — Geometry and Ornament in Islamic Architecture.
The Getty Center for the History of Art and the Humanities, 1995.

[117] John Allen Paulos. Mathematics and Humor. The University of Chicago Press, 1980.

[118] Roger Penrose. Escher and the visual representation of mathematical ideas. In H. S. M. Cox-
eter et al., editor, M.C. Escher: Art and Science, pages 143–157. Elsevier Science Publishers
B.V., 1986.

[119] Ivars Peterson. The Mathematical Tourist: Snapshots of Modern Mathematics. W. H. Free-
man and Company, New York, 1988.

[120] William H. Press, Saul A. Teukolsky, William T. Vetterling, and Brian P. Flannery. Numerical
Recipes in C: The Art of Scientific Computing. Cambridge University Press, second edition,
1992. ISBN 0-521-43108-5. Held in Cambridge.208

[121] A. Racinet. The Encyclopedia of Ornament. Studio Editions, 1988.

[122] J. F. Rigby. Butterflies and snakes. In H. S. M. Coxeter et al., editor, M.C. Escher: Art and
Science, pages 211–220. Elsevier Science Publishers B.V., 1986.

[123] Doris Schattschneider. Escher’s classification system for his colored periodic drawings. In
H. S. M. Coxeter et al., editor, M.C. Escher: Art and Science, pages 82–96. Elsevier Science
Publishers B.V., 1986.

[124] Doris Schattschneider. M.C. Escher: Visions of Symmetry. W.H. Freeman, 1990.

[125] P. J. Schneider. An algorithm for automatically fitting digitized curves. In Graphics Gems,
pages 612–626. Academic Press, Boston, 1990.

[126] G. C. Shephard. What Escher might have done. In H. S. M. Coxeter et al., editor, M.C. Es-
cher: Art and Science, pages 111–122. Elsevier Science Publishers B.V., 1986.

[127] A. V. Shubnikov and V. A. Koptsik. Symmetry in Science and Art. Plenum Press, 1974.

[128] Peter Stampfli. New quasiperiodic lattices from the grid method. In Istv ́an Hargittai, editor,
Quasicrystals, Networks and Molecules of Fivefold Symmetry, chapter 12, pages 201–221.
VCH Publishers, 1990.

[129] Desmond Stewart. The Alhambra. Newsweek, 1974.

[130] Ian Stewart. The Problems of Mathematics. Oxford University Press, 1987.

[131] Peter G. Szilagyi and John C. Baird. A quantitative approach to the study of visual symmetry.
Perception & Psychophysics, 22(3):287–292, 1977.

[132] C. W. Tyler. The human expression of symmetry:Art and neuroscience.
http://www.ski.org/CWTyler_lab/CWTyler/Art\%20Investigations/Symmetry/S%ymmetry.html.

[133] Shinji Umeyama. Least-squares estimation of transformation parameters between two point
patterns. IEEE Transactions on Pattern Analysis and Machine Intelligence, 13(4):376–380,
April 1991.

[134] David Wade. Pattern in Islamic Art. The Overlook Press, 1976.

[135] Dorothy K. Washburn and Donald W. Crowe. Symmetries of Culture. University of Wash-
ington Press, 1992.

[136] Magnus J. Wenninger. Polyhedron Models. Cambridge University Press, 1971.209

[137] Hermann Weyl. Symmetry. Princeton Science Library, 1989.

[138] Stephen Wolfram. A New Kind of Science. Wolfram Media, Inc., 2002.

[139] Michael T. Wong, Douglas E. Zongker, and David H. Salesin. Computer–generated floral
ornament. Proceedings of SIGGRAPH’98, pages 423–434, 1998.

[140] Jane Yen and Carlo S ́equin. Escher sphere construction kit. In Proceedings of the 2001
symposium on Interactive 3D graphics, pages 95–98. ACM Press, 2001.

[141] Douglas Zongker. Celtic knot thingy. http://www.cs.washington.edu/homes/dougz/hacks/knot/.

[142] Douglas Zongker. Creation of overlay tilings through dualization of regular networks. In
Nathaniel Friedman and Javiar Barrallo, editors, ISAMA 99 Proceedings, pages 495–502,
1999.

== Links ==
=== Full Text ===
http://grail.cs.washington.edu/theses/KaplanPhd.pdf

[[intern file]]

=== Sonstige Links ===
http://www.cgl.uwaterloo.ca/~csk/phd/

http://www.cgl.uwaterloo.ca/~csk/

http://www.cgl.uwaterloo.ca/~csk/pubs.html

http://www.cgl.uwaterloo.ca/~csk/projects/

@@ Zeile 2: / Zeile 2: @@
 == Reference ==
-Craig S. Kaplan: Computer Graphics and Geometric Ornamental Design. Ph.D. Thesis, University of Washington, 2002.
+[[Craig S. Kaplan]]: Computer Graphics and Geometric Ornamental Design. Ph.D. Thesis, University of Washington, 2002.
 == DOI ==

@@ Zeile 30: / Zeile 30: @@
 == Used References ==
-[1] Jan Abas. A hyperbolic mural. http://www.bangor.ac.uk/~mas009/ppic7.html.
+[1] Jan Abas. A hyperbolic mural. http://www.bangor.ac.uk/~mas009/ppic7.html. 404
 [2] Syed Jan Abas and Amer Shaker Salman. Symmetries of Islamic Geometrical Patterns. World
 Scientific, 1995.
-[3] Steve Abbott. Steve Abbott’s computer drawn Celtic knotwork. http://www.abbott.demon.co.uk/knots.html.
+[3] Steve Abbott. Steve Abbott’s computer drawn Celtic knotwork. http://www.abbott.demon.co.uk/knots.html. 404
 [4] Maneesh Agrawala and Chris Stolte. Rendering effective route maps: Improving usability
 through generalization. Proceedings of SIGGRAPH 2001, pages 241–250, 2001.
-[5] Nina Amenta and Mark Phillips. Kali. http://www.geom.umn.edu/java/Kali/.
+[5] Nina Amenta and Mark Phillips. Kali. http://www.geom.umn.edu/java/Kali/. 404
 [6] E. M. Arkin, L. P. Chew, D. P. Huttenlocher, K. Kedem, and J. S. B. Mitchell. An efficiently
@@ Zeile 58: / Zeile 58: @@
 [11] Jinny Beyer. Designing Tesselations: The Secrets of Interlocking Patterns. Contemporary
 Books, 1999.
-[12] Jay Bonner. Geodazzlers. http://www.dstoys.com/GD.html.
+[12] Jay Bonner. Geodazzlers. http://www.dstoys.com/GD.html. 404
 [13] Jay Francis Bonner. Islamic Geometric Patterns: Their Historical Development and Tradi-
@@ Zeile 202: / Zeile 202: @@
 W. H. Freeman and Company, third edition, 1993.
-[63] Bathsheba Grossman. Bathsheba Grossman – sculpting geometry. http://www. bathsheba.com/.
+[63] Bathsheba Grossman. Bathsheba Grossman – sculpting geometry. http://www.bathsheba.com/.
 [64] Branko Gr ̈unbaum. The emperor’s new clothes: Full regalia, G string, or nothing?
@@ Zeile 237: / Zeile 237: @@
 Press, New York, second edition, 1995.205
-[75] George W. Hart. Conway notation for polyhedra. http://www.georgehart.com/
+[75] George W. Hart. Conway notation for polyhedra. http://www.georgehart.com/virtual-polyhedra/conway_notation.html.
 [76] George W. Hart. Geometric sculpture. http://www.georgehart.com/sculpture/sculpture.html.
@@ Zeile 274: / Zeile 273: @@
 [88] Washington Irving. The Alhambra. Macmillan and co., 1931.
-[89] Drew Ivans. The origin and meaning of Celtic knotwork. http://www.craytech.com/drew/knotwork/knotwork-meaning.html.206
+[89] Drew Ivans. The origin and meaning of Celtic knotwork. http://www.craytech.com/drew/knotwork/knotwork-meaning.html 404
 [90] Robert Jensen and Patricia Conway. Ornamentalism: the New Decorativeness in Artchitec-
@@ Zeile 281: / Zeile 280: @@
 [91] Owen Jones. The Grammar of Ornament. Studio Editions, 1986.
-[92] Craig S. Kaplan. isohedral.ih. http://www.cs.washington.edu/homes/csk/tile/escherization.html.
+[92] Craig S. Kaplan. isohedral.ih. http://www.cs.washington.edu/homes/csk/tile/escherization.html => http://www.cgl.uwaterloo.ca/~csk/projects/escherization/
 [93] Craig S. Kaplan. Computer generated islamic star patterns. In Reza Sarhangi, editor, Bridges
@@ Zeile 287: / Zeile 286: @@
 [94] Craig S. Kaplan. Computer generated islamic star patterns. Visual Mathematics, 2(3), 2000.
-http://members.tripod.com/vismath4/kaplan/index.html.
+http://members.tripod.com/vismath4/kaplan/index.html
 [95] Craig S. Kaplan and George W. Hart. Symmetrohedra: Polyhedra from symmetric placement
@@ Zeile 303: / Zeile 302: @@
 [99] A.J. Lee. Islamic star patterns. Muqarnas, 4:182–197, 1995.
-[100] Raph Levien. libart. http://www.levien.com/libart/.
+[100] Raph Levien. libart. http://www.levien.com/libart/
 [101] Silvio Levy. Automatic generation of hyperbolic tilings. In Michele Emmer, editor, The
@@ Zeile 333: / Zeile 332: @@
 [110] Scott McCloud. Understanding Comics. HarperCollins, 1993.
-[111] Christian Mercat. Celtic knotwork, the ultimate tutorial. http://www.entrelacs.
+[111] Christian Mercat. Celtic knotwork, the ultimate tutorial. http://www.entrelacs.net/en.index.html
-[112] Kevin Mitchell. Semi-regular tilings of the plane. mitchell/tilings/Part1.html. http://people.hws.edu/
+[112] Kevin Mitchell. Semi-regular tilings of the plane. http://people.hws.edu/mitchell/tilings/Part1.html
 [113] Anders Pape Møller and John P. Swaddle. The biological importance of imperfect symmetry.
 In Asymmetry, Developmental Stability and Evolution, chapter W1. Oxford University Press,
-. Available online from http://www.oup.co.uk/isbn/0-19-854894-X.
+. Available online from http://www.oup.co.uk/isbn/0-19-854894-X
 [114] E. N. Mortenson and W. A. Barrett. Intelligent scissors for image composition. Proceedings
 of SIGGRAPH 1995, pages 191–198, 1995.
-[115] Joseph Myers. Polyomino, polyhex, and polyiamond tiling. http://www.srcf.ucam.org/~jsm28/tiling/.
+[115] Joseph Myers. Polyomino, polyhex, and polyiamond tiling. http://www.srcf.ucam.org/~jsm28/tiling/
 [116] G ̈ulru Necipoˇglu. The Topkapı Scroll — Geometry and Ornament in Islamic Architecture.
@@ Zeile 394: / Zeile 392: @@
 [132] C. W. Tyler. The human expression of symmetry:Art and neuroscience.
-http://www.ski.org/CWTyler_lab/CWTyler/Art\%20Investigations/Symmetry/S%ymmetry.html.
+http://www.ski.org/CWTyler_lab/CWTyler/Art\%20Investigations/Symmetry/S%ymmetry.html 404
 [133] Shinji Umeyama. Least-squares estimation of transformation parameters between two point
@@ Zeile 417: / Zeile 415: @@
 symposium on Interactive 3D graphics, pages 95–98. ACM Press, 2001.
-[141] Douglas Zongker. Celtic knot thingy. http://www.cs.washington.edu/homes/dougz/hacks/knot/.
+[141] Douglas Zongker. Celtic knot thingy. http://www.cs.washington.edu/homes/dougz/hacks/knot/ 404
 [142] Douglas Zongker. Creation of overlay tilings through dualization of regular networks. In

@@ Zeile 203: / Zeile 203: @@
 [63] Bathsheba Grossman. Bathsheba Grossman – sculpting geometry. http://www. bathsheba.com/.
 [64] Branko Gr ̈unbaum. The emperor’s new clothes: Full regalia, G string, or nothing?
 Mathematical Intelligencer, 6(4):47–53, 1984.
 [65] Branko Gr ̈unbaum. Periodic ornamentation of the fabric plane: Lessons from Peruvian fab-
@@ Zeile 424: / Zeile 422: @@
 Nathaniel Friedman and Javiar Barrallo, editors, ISAMA 99 Proceedings, pages 495–502,
 .
 == Links ==