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Planar Subdivisions by Radical Axes Applied to Structural Morphology

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Computational Science and Its Applications — ICCSA 2003 (ICCSA 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2669))

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Abstract

In previous articles the relation between Lattice and Plate structural systems to Delaunay and Voronoi planar diagrams has been demonstrated. The present contribution shows how Geotangent Mesh designs can also be formulated as a bi-dimensional problem stated as the Planar Subdivision of Radical Axes arising from a packing of circles. This way the origin of all of the Spatial Mesh Structural Typologies can be formulated by means of the basic elements of Computational Geometry.

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References

  1. Alvaro J. I., Otero C. Designing optimal spatial meshes: cutting by parallel trihedra procedure. IASS Journal (International Association for Shell and Spatial Structures) VOL. 41 (2000) N. 133.

    Google Scholar 

  2. Coxeter H. S. M. Regular Complex Polytopes. Ed. Cambridge University Press. 1974. 9–11.

    Google Scholar 

  3. Critchlow, K. Order in Space. Ed. Thames and Hudson. 1969. 75–77

    Google Scholar 

  4. Davis, W.E., Yacoe J., “A New Polyhedral Approximation to an Ellipsoid of Revolution”. International Journal of Space Structures, Vol. 5,nr. 3 & 4. 1990.

    Google Scholar 

  5. Edelsbrunner H., Sheidel R. “Voronoi Diagrams and Arrangements”. Discrete Computational Geometry 1, 25–44 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  6. Fuller B., U.S. Patent 2,682,235 6/1954

    Google Scholar 

  7. Makowski, Z.S. Analysis, Design and Construction of Braced Domes. Cambridge University Press. Great Britain, 1984.

    Google Scholar 

  8. Margarit J., Buxadé C. Las Mallas Espaciales en Arquitectura. Ed. Gustavo Gili.1972.

    Google Scholar 

  9. Otero C., Gil V., Alvaro J. I. CR-Tangent Meshes. IASS Journal VOL. 41 (2000) n. 132. 41–48.

    Google Scholar 

  10. Otero C. Diseño Geométrico de Cúpulas no esféricas aproximadas por mallas triangulares con un número mínimo de longitudes de barra. Ph D. University of Cantabria. 1990. Not available, contact the author.

    Google Scholar 

  11. Otero C., Togores R. “Computational Geometry and Spatial Meshes”. Lecture Notes On Computer Science 2002. Vol. 2. Springer. 2002.

    Google Scholar 

  12. Pearce P. Structure in Nature is a Strategy for Design. Ed. Cambridge University Press. 1974

    Google Scholar 

  13. Preparata F, Shamos I. “Computational Geometry: An Introduction”. Springer. 1985. 244–247.

    Google Scholar 

  14. Pedoe, D. “Geometry: a comprehensive course”. Cambridge Univ. Press. 1970. 71–121.

    Google Scholar 

  15. Tsuboi Y. Analysis, design and realization of space frames. (Working Group of Spatial Steel Structures). IASS Bulletin, No 84. April 1984 and No 96, April 1988. 11–30.

    Google Scholar 

  16. Wester, T. “A Geodesic Dome-Type Based on Pure Plate Action”. International Journal of Space Structures, Vol. 5,nr. 3 & 4. 1990. 155–167

    Google Scholar 

  17. Wester, T. “The Structural Morphology of Basic Polyhedra”, Chapter 11 in “Beyond The Cube”, pp. 301–342. John Wiley & Sons. 1997. 301–342

    Google Scholar 

  18. Yacoe J. U.S. Patent 4,679,361 7/1987

    Google Scholar 

  19. Yacoe J. U.S. Patent 4,825602 5/1989

    Google Scholar 

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Author information

Authors and Affiliations

  1. EGI-CAD Research Group. Department of Geographical Engineering and Graphic Expression Techniques, University of Cantabria, Spain

    R. Togores & C. Otero

Authors
  1. R. Togores
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  2. C. Otero
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Editor information

Editors and Affiliations

  1. Army High Performance Computing Research Center, USA University of Minessota Department of Computer Science and Engineering, MN, 55455, USA

    Vipin Kumar

  2. Department of Computer Science, University of Calgary, Calgary, AB, T2N1N4, Canada

    Marina L. Gavrilova

  3. Heuchera Technologies Inc., 122 9251-8Yonge Street, Richmond Hill, ON, Canada, L4C 9T3

    Chih Jeng Kenneth Tan

  4. School of Computer Science, The Queen’s University of Belfast, Belfast, BT7 1NN, Northern Ireland UK

    Chih Jeng Kenneth Tan

  5. Département d’informatique et de recherche opérationelle Montréal, Université de Montréal, Québec, H3C 3J7, Canada

    Pierre L’Ecuyer

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© 2003 Springer-Verlag Berlin Heidelberg

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Togores, R., Otero, C. (2003). Planar Subdivisions by Radical Axes Applied to Structural Morphology. In: Kumar, V., Gavrilova, M.L., Tan, C.J.K., L’Ecuyer, P. (eds) Computational Science and Its Applications — ICCSA 2003. ICCSA 2003. Lecture Notes in Computer Science, vol 2669. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44842-X_45

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  • DOI: https://doi.org/10.1007/3-540-44842-X_45

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40156-8

  • Online ISBN: 978-3-540-44842-6

  • eBook Packages: Springer Book Archive

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