Unconventional building forms roofed with innovative structures arranged on regular surfaces with the negative Gaussian curvature

A novel method for shaping innovative building forms, roofed with diversified complex continuous and discontinuous folded structures composed of many transformed corrugated shell units, is presented in the paper. The units are defined on the basis of specific reference polyhedral networks and arranged on arbitrary reference surfaces characterized by the negative Gaussian curvature. The method is presented using several computer models of complex building structures with folded plane-walled elevations. The proposed method significantly supplements the previous method developed for modelling building free forms, roofed with shell structures arranged in conformity with surfaces having the positive Gaussian curvature. Some basic rules using parameterization and governing the creation of the multi-plane elevations, ribbed continuous and discontinuous roof shell structures, arranged in different unconventional and visually attractive patterns, were developed. The elaborated specific sets of division coefficients are taken as parameters for the designed building structures. These sets determine unconventional polyhedral networks, which are composed of several specific sets that allow to define a polygonal eaves network, a reference surface and, finally, individual shell units of the roof structures. The developed method is presented using the example of three novel forms defined by means of the appropriately selected diversified sets of values of the division coefficients. The elaborated new forms confirm the innovative nature of the achieved results. By imposing appropriate proportions between the values of these division coefficients, the developed method enables the creation of two different groups continuous and discontinuous complex shell roof structures.