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
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.
Coxeter H. S. M. Regular Complex Polytopes. Ed. Cambridge University Press. 1974. 9–11.
Critchlow, K. Order in Space. Ed. Thames and Hudson. 1969. 75–77
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.
Edelsbrunner H., Sheidel R. “Voronoi Diagrams and Arrangements”. Discrete Computational Geometry 1, 25–44 (1986)
Fuller B., U.S. Patent 2,682,235 6/1954
Makowski, Z.S. Analysis, Design and Construction of Braced Domes. Cambridge University Press. Great Britain, 1984.
Margarit J., Buxadé C. Las Mallas Espaciales en Arquitectura. Ed. Gustavo Gili.1972.
Otero C., Gil V., Alvaro J. I. CR-Tangent Meshes. IASS Journal VOL. 41 (2000) n. 132. 41–48.
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.
Otero C., Togores R. “Computational Geometry and Spatial Meshes”. Lecture Notes On Computer Science 2002. Vol. 2. Springer. 2002.
Pearce P. Structure in Nature is a Strategy for Design. Ed. Cambridge University Press. 1974
Preparata F, Shamos I. “Computational Geometry: An Introduction”. Springer. 1985. 244–247.
Pedoe, D. “Geometry: a comprehensive course”. Cambridge Univ. Press. 1970. 71–121.
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.
Wester, T. “A Geodesic Dome-Type Based on Pure Plate Action”. International Journal of Space Structures, Vol. 5,nr. 3 & 4. 1990. 155–167
Wester, T. “The Structural Morphology of Basic Polyhedra”, Chapter 11 in “Beyond The Cube”, pp. 301–342. John Wiley & Sons. 1997. 301–342
Yacoe J. U.S. Patent 4,679,361 7/1987
Yacoe J. U.S. Patent 4,825602 5/1989
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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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