Geometry of Fabrics Bibliography (8/18/99)
Mathematics and Computing Department
York College (CUNY)
Jamaica, New York 11451-0001
Email: email@example.com (for additions, suggestions, and corrections)
Astle, B., Pantactic squares, Math. Gazette 49 (1965) 144-52.
Aubry, A., Les principes de la géométrie des quinconces, Ensign. Math. 13 (1911) 187-203.
Bouwkamp, C., and P. Janssen, A. Koene, Note on pantactic squares, Math. Gazette 54
Clapham, C., When a fabric hangs together, Bull. London Math. Soc., 12 (1980) 161-164.
Clapham, C., The bipartite tournament associated with a fabric, Discrete Math. 57
Clapham, C., When a three-way fabric hangs together, JCT, Series B, 38 (1985) 190.
Coxeter, H., Colored symmetry, in H. Coxeter et al. (eds.), M.C. Escher: Art and Science,
Elsevier, North-Holland, Amsterdam, 1986, p. 15-33.
Dass, B., Generative technique for weave design: application of layer symmetry theories
to weave design, PhD Thesis, Ulster, 1989.
Dass, B., Mataphorical weaves: applications of rules of anti-symmetry to weave design,
Ars Textrina 19 (1993) 61-73.
Delaney, C., When a fabric hangs together, Ars Combinatoria 21-A (1986) 71-79.
Enns, T., An efficient algorithm determining when a fabric hangs together, Geom. Dedicata
15 (1984) 259-260.
Fielker, D., Weaving tessellations, Part 1: Two-way weaves, Mathematics Teaching
91 (1980) 34-39.
Fielker, D., Weaving tessellations, Part 2: Three-way weaves, Mathematics Teaching
91 (1980) 40-43.
Freeman, W., and L. Peters, A method of weave-coding: Part I, Journal of the Textile
Institute, 58 (1967) 639-650.
Grünbaum, B., and G. Shephard, Satins and twills: an introduction to the geometry
of fabrics, Math. Magazine 53 (1980) 139-161.
Grünbaum, B., and G. Shephard, Tilings, patterns, fabrics and related topics in discrete
geometry, Jahresber. Deutsch. Math. Verein. 85 (1983) 1-32.
Grünbaum, B., and G. Shephard, Geometry of Fabrics, in Geometrical Combinatorics,
F. Holroyd and R. Wilson, (eds.), Pitman, 1984, p. 77-97.
Grünbaum, B., and G. Shephard, A catalogue of isonemal fabrics, Annals of the New
York Academy of Sciences, 440 (1985) 279-298.
Grünbaum, B., and G. Shephard, An extension to the catalogue of isonemal fabrics,
Discrete Math. 60(1986) 155-192.
Grünbaum, B., and G. Shephard, Isonemal fabrics, Amer. Math. Monthly, 95 (1988) 5-30.
Grünbaum, B., and G. Shephard, Geometry of fabrics, Abstract 757-D1, Notices of the
Amer. Math. Soc., 25 (1978), A-462.
Hann, M., and G. Thomson, Geometry of regular repeating patterns, Textile Progress
Series, 22 (1), The Textile Institute, Manchester, 1992.
Hoskins, J., Pattern Master II, released Aug. 1982, distributor The Looms, Mineral
Hoskins, J., Computerized fabric analysis, Shuttle, Spindle and Dyepot 13 (1982) 26-27.
Hoskins, J., Binary interlacement arrays and structural cross-sections, Congressus
Numerantium 40 (1983) 63-76.
Hoskins, J., Factoring binary matrices: a weaver's approach, Lecture Notes in Mathematics,
Vol. 952, Springer-Verlag, New York, 1983, 300-326.
Hoskins, J., Multi-layered cloths: A structured approach, Ars Textrina 1 (1983) 137-158.
Hoskins, J., Isonemal arrays and textile computer graphics, Ph. D. Thesis, University
of Manitoba, Departments of Clothing and Textiles and Computer Science, 1985.
Hoskins, J., Automatic analysis of coloured images, Ars Textrina 5 (1986) 151-166.
Hoskins, J., and W. Hoskins, The solutions of certain matrix equations arising from
the structural analysis of woven fabrics, Ars Combinatoria 11 (1981) 51-59.
Hoskins, J., and W. Hoskins, A faster algorithm for factoring binary matrices, Ars
Combinatoria 16-B (1983) 341-350.
Hoskins, J. and W. Hoskins, Algorithms for the design and analysis of woven textiles,
Proceedings of the 1983 ACM Conference on Personal and Small Computers, p. 153-160.
Hoskins, J. and W. Hoskins, An improved algorithm for factoring binary interlacement
matrices, Ars Combinatoria 41 (1984) 302-303.
Hoskins, J. and W. Hoskins, A. Street, R. Stanton, Some elementary isonemal binary
matrices, Ars Combinatoria 13 (1982) 3-38.
Hoskins, J., and M. King, An interactive database for woven textile design, Proceedings
of the Textile Institute Annual Conference, Hong Kong, 1984.
Hoskins, J., and M. King, Interactive design of woven textiles, Proceedings of the
International Computer Color Graphics Conference, Tallahassee, Florida, 1983.
Hoskins, J., and C. Praeger, A. Street, Twills with bounded float length, Bull. Australian
Math. Soc. 28 (1983) 255-281.
Hoskins, J., and C. Praeger, A. Street, Balanced twills with bounded float-length,
Cong. Num. 40 (1983) 77-89.
Hoskins, J., and R. Stanton, A. Street, Enumerating the compound twillins, Congressus
Numerantium 38 (1983) 3-22.
Hoskins, J., and R. Stanton, A. Street, The compound twillins: reflection at an element,
Ars Combinatoria 17 (1984) 177-190.
Hoskins, J., and A. Street, R. Stanton, Binary interlacement arrays and how to find
them, Congressus Numerantium 42 (1984) 321-376.
Hoskins, J. and R. Thomas, The patterns of the isonemal two-color two-way two-fold
fabrics, Bull. Australian Math. Soc., 44 (1991) 33-43.
Hoskins, W., An Improved Algorithm for Factoring Binary Matrices, Second West Coast
Conference on Computing in Graph Theory, Eugene, Oregon, June, 1983.
Hoskins, W., and J. Hoskins, Satin and long-eyed heddles, Weavers Journal, 6 (1981)
Hoskins, W., and J. Hoskins, Using a microcomputer for the design and analysis of
woven textiles, Presented at ACM SIGSMALL/PC Conference, San Diego, December, 1983.
Hoskins, W., and J. Hoskins, Design of interactive systems for real-time dobby control,
Ars Textrina 5 (1986) 33-50.
Hoskins, W., and J. Hoskins, M. King, A microcomputer controlled dobby loom for textile
prototyping, Presented at the International Symposium on Fiber Science Technology,
Hakone, Japan, August, 1985.
Hoskins, W., and J. Hoskins, J. May, Algorithms for colour analysis, Proceedings of
the 1985 ACM Conference on Personal and Small Computers, Boston, May, 1985.
Hoskins, W., and J. Hoskins, G. McMaster, Simulation of interlaced arrays, Part 1,
ISMM, International Conference on the Application of Microcomputers, New York, 1984.
Hoskins, W., and J. Hoskins, C. Zarnke, An object-oriented textile design and production
environment, 6th International Conference in Computer Science, Santiago, Chile, 1986.
Hoskins, W., and J. Hoskins, C. Zarnke, Interactive computer graphic control in a
dobby production environment, HCI International '87, Second International Conference
on Human-Computer Interaction, Honolulu, Hawaii, Aug. 1987.
Hoskins, W., and J. Schwartzman, Compound colour Isonemality, Presented at the Spring
Maniwat Conference, St. Pierre, 1984.
Hoskins, W., and A. Street, Twills on a given number of harnesses, J. Australian Math.
Soc. (Ser. A), 33 (1982) 1-15.
Hoskins, W., and R. Thomas, Compound isonemality of binary arrays, presented at 8th
British Conference on Combinatorial Mathematics, U. of Swansea, 1981.
Hoskins, W., and R. Thomas, Conditions for isonemal arrays on a Cartesian grid, Lin.
Algebra and Appl. 57 (1984) 87-103.
Litvin, D. and T. Wike, Character Tables and Compatibility Relations of the Eighty
Layer Groups, Plenum Press, New York, 1991.
Lourie, J., and J. Lorenzo, A. Bomberault, On-line textile designing, Proceedings
of the ACM Natinal Meeting, 1966, p. 537.
Lourie, J., and A. Bonin, Computer -Controlled Textile Designing and Weaving, Proceedings-IFIPS
(1968) p. 884.
Lourie, J., Loom-constrained designs: an algebraic solution, Proceedings ACM National
Conference, 1969, p. 185-192.
Lourie, J., TextileGraphics/Computer Aided, Fairchild Publications, New York, 1973.
Lucas, E., Application de L'Arithmétique àla Construction de l'Armure des Satins Réguliers,
Lucas, E., Le principes fondamentaux de la géometrie des tissus, Compte Rendu del
l'Association Francasise four l'Avancement des Sciences 40 (1911) 72-88.
Montfort, F., and M. Belly, Mathematical and informational aspects of simple weaves
of fabric, Part 1: Mathematical definition of the simple weaves of fabrics, Proceedings
of the 9th International Wool Textile Research Conference, Volume iv, 1995, p. 160-171.
Montfort, F., and M. Belly, Mathematical and informational aspects of the simple weaves
of fabric, Part 2: Inventory of fundamental simple weaves by a computer program,
Proceedings of the 9th International Wool Textile Research Conference, Volume iv,
1995, p. 172-184.
Murphy, J., A Treatise on the Art of Weaving with Calculations and Tables for the
Use of Manufacturers, Blackie & Son, Glasgow, 1836.
Newton, A., and B Sarkar, An analysis of compound weaves, J. Text. Inst. 10 (1979)
Nishikawa, S., Automatic patterning technique on Jacquard Weaving Process, Bulletin
of Research Institute for Polymers and Textiles, No. 105, (1974) 5.
Pedersen, J., Some isonemal fabrics on polyhedral surfaces, The Geometric Vein, The
Coxeter Festschrift, (ed. C. Davis, B. Grünbaum, and F. Sherk, Springer-Verlag, New
York, 1981, 99-122.
Pedersen, J., Geometry: The unity of theory and practice, Mathematical Intelligencer
5 (1983) 37-47.
Robinson, A., and R. Marks, Woven Cloth Construction, The Textile Institute, Manchester,
Roth, R., The symmetry groups of periodic isonemal fabrics, Geometricae Dedicata 48
Scivier, J., and M. Hann, The application of layer symmetry principles to the classification
of fundamental simple weaves, University of Leeds, preprint.
Shorter, S., The mathematical theory of sateen arrangement, Math. Gazette 10 (1920)
Steggall, J., On the numbers of patterns that can be derived from certain elements,
Messenger of Math. 37 (1908) 56-61.
Street, A., and S. Oates, Balanced binary arrays I: The square grid, in Combinatorial
Mathematics Vi, Proc. 6th Australian Conference, Lecture Notes in Mathematics, Vol. 748, ed. A. Horadam and W. Wallis, Springer-Verlag, New York, 1979, p. 165-198.
Thomas, R., Perfect Colorings of Isonemal fabrics by thin striping, Bull. Australian Math., 83 (2011) 63-86.
Wood, E., The 80 diperiodic groups in three dimensions, Bell Telephone System Technical
Publication, Monograph 4680, 1964.
Woods, J., The geometrical basis of pattern design, Textile Institute of Manchester
Journal 26 and 27 (1935 and 1936) (Section 2, Transactions): Part I - Point and line
symmetry in simple figures and borders, T197-210; Part II - Nets and sateens, T293-308; Part III - Geometrical symmetry in plane patterns, T341-T357, Part iv - Counterchange
symmetry in plane patterns, T 305-320.
I wish to thank B. Grünbaum, M. Hann, J. Sciever, J. Hoskins, W. Hoskins, and R. Stanton for making
available to me materials that led to additional listings in this bibliography.
Some of this work was prepared with partial support from the National Science Foundation
(Grant Number: DUE 9555401) to the Long Island Consortium for Interconnected Learning
(administered by SUNY at Stony Brook, Alan Tucker, Project Director).
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