MODELING ARCHITECTURAL FORM SURFACE DEPENDENT SECTIONS
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Abstract
For the design of surfaces in architecture, as a rule, universal techniques developed for other technical industries are used. First of all, these are general kinematic surfaces and interpolation cubic splines for modeling complex piecewise smooth surfaces. The authors propose to use the fourth degree inerodifferential spline developed by them for problems of geometric modeling of architectural forms. For calculations and constructions on a computer, the proposed spline is not much more complicated than traditional cubic splines, since it has one additional parameter - a coefficient. However, this allows you to locally control the shape of a curve or surface during design, that is, to change the shape in individual areas without affecting other areas. The article proposes a method for constructing a geometric model of the kinematic surface of dependent sections with a fourth degree parabola as a generator. When using cubic splines as a guide, the surface is a 3 × 4 non-uniform (heterogeneous) spline. The article shows that the surface on the basis of the proposed mathematical apparatus can be composite piecewise-smooth. A particular case of surface design is considered on the example of creating a model of the surface of the facade of a residential building according to the existing concept. The algorithm can be easily programmed and added as a tool to existing CAD systems.
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References
Ivanov G.S. Konstruirovanie tehnicheskih poverhnostej (matematicheskoe modelirovanie na osnove nelinejnyh preobrazovanij) [Technical surface’s construction (mathematic modeling on based nonlinear transformation)]/ Moscow, Mashinostroenie Pub., 1987, 192 p.
Korotkiy V., Usmanova E., Khramova L., Komp’juternoe modelirovanie kinematicheskih poverhnostej [Computer simulation of Kinematic Surfaces]. 2016, v/ 3, i. 4, pp. 19-26.
Girn A.G. Kriterii vybora sposoba konstruirovanija obvoda. Kn.: Avtomati-zacija tehnologicheskoj podgotovki proizvodstva na baze sistem avtomatizacii prektirvanija [Criteria for choosing a path design method. Vol.: Automation of technological preparation of production based on automation systems for shutting down]. Omsk, 1980, pp. 97-101.
Osipov V.A., Leljushenko S.I., Chistjakov F.K. Analiticheskoe opisanie ajerodinamicheskih poverhnostej metodom special'nogo kontura. Kn. 3: Mashinnoe proektirovanie, uvjazka i vosproizvedenie slozhnyh detalej v aviastroenii. [Analytical description of aerodynamic surfaces using the special contour method. Vol. 3: Machine design, linking and reproduction of complex parts in aircraft construction]. Irkutsk, 1976, pp. 68-70.
Osipov V.A. SAPR i inzhenerno-geometricheskie zadachi aviacionnoj tehniki. Izv. vyssh. uchebn. zavedenij. Aviac. Tehnika [CAD and engineering and geometric problems of aviation technology. News vysh. educational institutions. Aviation technology]. 1980, Vol. 2, pp. 119-122.
Rejnov M.N. Matematicheskaja model' sudovoj poverhnosti [Mathematical model of the ship's surface]. L.: Sudostroenie, 1977. 32 p.
Krivoshapenko S.N., Ivanov V.N. Entsiklopedia analiticheskih poverhnostej [Encyclopedia of analytical surfaces]. Moscow. Librokom Publ., 2010. 560 p.
Krivoshapenko S.N. Postroyeniye, raschet i vozmozhnost' primeneniya torsovykh obolochek v tonkostennykh konstruktsiyakh (Construction, calculation and the possibility of using torso shells in thin-walled structures)// Raschet obolochek stroitel'nykh konstruktsiy. – М.: ed. UDN, 1982. – pp. 54-66
Avdot'in L.N. Matematika i elektronno-vychislitel'naya tekhnika v reshenii prikladnykh gradostroitel'nykh zadach. (Mathematics and computer technology in solving applied urban planning problems.) – М.: TSNTI gosgrazhdanstroya, 1966
Dergunov V.I., Zhilina N.D., Popov E.V. Osnovy komp'yuternykh tekhnologiy v proyektirovanii (Fundamentals of computer technology in design) – N.Novgorod: Pub. NNGASU, 2003. – 157 p.
Chekalin A. A., Reshetnikov M. K., Zajcev Ju. A. Modelirovanie kusochno-gladkoj poverhnosti dvumernym splajnom razlichnyh stepenej. Nauchno-metodicheskie problemy graficheskoj podgotovki v tehnicheskom vuze na sovremennom jetape: materialy nauch.-metod. konf. po-svjashh. 80-letiju AGTU [Modeling a piecewise-smooth surface with a two-dimensional spline of various degrees. Scientific and methodological problems of graphic training in a technical university at the present stage: materials scientific method. conf. dedicated 80th anniversary of AGTU]. Astrahan', 15-17 sent. 2010, AGTU pp. 200-206.
Foks A., Pratt M. Vychislitel’naja geometrija. Primenenie v proektirovanii I na proizvodstve [Computing Geometry in Design and Production]. Moscow, Mir Publ. 1982, 304 p.