The mathematical and computer modelling of the building constructions on the R-functions basis

Abstract

In Amsterdam the team of architects (DUS Architects) works above the project, called to master one of the most important directions of development of a three-dimensional printing - the construction of buildings. In China (Yingchuang New Materials) the printer which is capable to print out small one- and two-storeyed houses has appeared. At the University of Southern California professor Behrokh Khoshnevis has developed the project of the three-dimensional printer, which is capable to "print" the two-storeyed house within only 24 hours. The one of methods of the decision of a problem of the printing information task is the R-functions theory application. The creation on the R-functions theory basis of the mathematical and computer model of a small country house as a whole is the purpose of the given paper. The most simple system R₀ is used for the required equations construction. In case of presence of translation along direct symmetry or cyclic type dot symmetry the superposition with corresponding periodic functions is used. Stage-by-stage construction of the all constructive building elements' equations is carried out: the base of walls, the partitions, the window and doorways, the roof including versatile one. Besides for the decoration of the house elevation the equations of various ornaments and columns are constructed for their subsequent realization on the 3D-printer. The analytical identification of the projected objects has enabled to use alphabetic geometrical parameters, that, in turn, has allowed to change operatively constructive elements of a house, that also is illustrated in this paper.