This research presents a descriptive geometric methodology for the generalized construction of non-ruled quadrics, emphasizing the definition of a generic polar system and its projective transformations. By extending traditional approaches beyond the limitations imposed by symmetry planes, the concept of the “generic polar system” enables the generation of theoretically infinite structural configurations. This innovative framework is designed to integrate effectively with 3D modeling software, offering advanced solutions for architectural and design applications.
PonceletJV.Traité des propriétés projectives des gures. Paris: Gauthier-Villars, 1822.
2.
MongeG.Geometrie descriptive: Le,ons donn’e aux’ Ecoles normales de l’an 3 de la Republique. Paris: Baudouin, 1799.
3.
SteinerJ.Systematische Entwicklung der Abh··angigkeit geometrischer Gestalten von einander. Leipzig: Engelmann, 1896.
4.
StaudtG.Geometrie der Lage. Nuremberg: Korn, 1847.
5.
StruikDJ.Lectures on classical differential geometry. Mineloa: Dover Publications, 1950.
6.
EnriquesF.Lezioni di geometria proiettiva. Bologna: Nicola Zanichelli, 1920, pp.254–256.
7.
GinoL.Complementi di geometria descrittiva. Milan: Hoepli, 1924, p.32.
8.
Martín-PastorA. Polyhedral transformation based on new rotational quadratic surface properties. In: Geometrias’19: Polyhedra and Beyond, Oporto, 5–7September2019. Oporto: Aproged.
9.
LeroyCFA.Traité de stéréotomie. Paris: Gauthier-Villars, 1870.
CremonaL.Elementi di geometria projettiva, vol. 1. Turin: Paravia e comp G.B, 1873, p.158.
12.
Martín-PastorANarvaez-RodriguezR.New properties about the intersection of rotational quadratic surfaces and their applications in architecture. Nexus Netw J2019; 21: 175–196.
13.
FiedlerWSaynoAPadovaE.Trattato di geometria descrittiva. Italy: Successori Le Monnier, 1874, p.88.
14.
CremonaL.Preliminari di una teoria geometrica delle superficie. Bologna: Gamberini e Parmeggiani, 1866, p.35.
15.
Di PaolaF. Costruzione omologica e rappresentazione digitale di una sezione conica. In: CarlevarisLDe CarloLMigliariR (eds) Attualità della Geometria descrittiva, vol. 2012-03. Roma: Cangemi Editore, 2012, pp.75–84.
