New applications of descriptive geometry: PQ meshes in contemporary architecture
DOI:
https://doi.org/10.6092/issn.1828-5961/3176Keywords:
descriptive geometry, architectural geometry, discrete differential geometry, free form surfaces, quad mesh, polyhedral, lines of curvatureAbstract
New modeling tools available for designers lead to big changes in the way architecture is done. One of the main application of descriptive Geometry is the approximation of continuous shapes in discrete surfaces called mesh. Every continuous surface can be tessellated in polyhedral surface with planar faces. Designers are becoming interested in quadrilateral planar mesh (PQ mesh) that can hold important offset properties. The study of quad mesh with planar faces in architecture seems to be the natural evolution of the important and ancient subject of polyhedra, brought back to vitality by the development of computers and that affects the entire discipline of descriptive Geometry.
References
Bogart, Andrew. Kocaturk, Tuba (2007), Free Form design as the digital “Zeitgeist”, in Journal of the International Association for Shell and Spatial Structures, Vol. 48 2007, pp 3-9.
Forster Kurt Walter (a cura di), (2004), Metamorph: Focus, in catalogo, La Biennale di Venezia, Marsilio ed., 2004, pp. 6-13.
Emmer, Michele, (2007), L’idea di spazio da Escher all’architettura virtuale, in De Carlo Laura, a cura di, Informatica e fondamenti scientifici della rappresentazione, Gangemi editore, 2007, pp 47-54.
Baglioni, Leonardo (2012), I poliedri e le tecniche di tassellazione delle superfici continue: un nuovo punto di incontro, in, Carlevaris Laura, De Carlo Laura, Migliari Riccardo, a cura di, Attualità della Geometria Descrittiva, Gangemi editore, 2012, pp 297-314.
Loria, Gino, (1935), Metodi Matematici, Hoepli, Milano.
Migliari, Riccardo (2008), Rappresentazione come sperimentazione, in Ikhnos analisi grafica e storia della rappresentazione, Lombardi editori, Siracusa 2008, pp. 11-28.
Migliari, Riccardo (2012), La Geometria descrittiva nel quadro storico della sua evoluzione dalle origini alla rappresentazione digitale, in, Carlevaris Laura, De Carlo Laura, Migliari Riccardo, a cura di, Attualità della Geometria Descrittiva, Gangemi editore, 2012, pp 15-42.
Sauer, Robert (1970), Differenzegeometrie, Springer, Berlin.
Pottmann, Helmut. Liu, Yang. Wallner, Johannes. Yang, Yong-Liang. Wang, Wenping (2006), Geometric modeling with conical meshes and developable surfaces, in ACM Trans. Graphics, Vol 25 n.3 2006, pp 681-689.
Pottmann, Helmut. Brell-Cokcan, Sigrid. Wallner, Johannes, (2006), Discrete Surfaces for Architectural Design, in Curves and Surface Design: Avignon 2006, Nashboro Press, 2007, pp 2123-234.
Pottmann, Helmut. Liu, Yang. Wallner, Johannes. Bobenko, Alexander. Wang, Wenping (2007), Geometry of Multi-layer Freeform Structures for Architecture, in ACM Trans. Graphics, Vol 26 n.3 2007, pp. 1-11.
Pottmann, Helmut. Asperl, A.. Hofer, M.. Kilian, A. (2007), Architectural Geometry, Bentley Institute Press.
Bobenko, Alexander. Suris, Yuri B.,(2008), Discrete Differential Geometry: Integrable Structure. Volume 98 of Graduate Studies in Mathematics, American Mathematical Society.
Martin, R. Raphael. de Pont J., Sharrock T. J. (1984), Cyclide surfaces in computer aided design, in The mathematics of surfaces, Ed. J. A. Gregory, Oxford University Press, pp 253–268.
Wang, Wenping. Wallner, Johannes. Liu, Yang (2006), An angle criterion for conical mesh vertices, in Geometry preprint 157, Vienna Univ. of Technology.
Fallavollita, Federico (2008), Le superfici rigate e le superfici sviluppabili. Una rilettura attraverso il laboratorio virtuale, Tesi di Dottorato di Ricerca in Scienze della Rappresentazione e del Rilievo, XXI ciclo, Sapienza Università di Roma, 2008.
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Copyright (c) 2012 Leonardo Baglioni