The problem of efficient design of roofs is a topical area of research. This is confirmed by scientific studies [1–5, etс.]. Today, in the times of information technology in all areas of actively using the computer and specific programs [6; 12; 15, etc.]. The author presents a proposal of geometric design (geometric solutions) for roofs with restrictions, so-called "roof with its neighbors."Roofs are treated as a special class of polyhedral surfaces. Construction includes a corresponding attachment roof with restrictions on the roof on a simple connection of the polygon, designing a conventional roof and perform the appropriate logic operation. Fig. 1. The Boolean operations are useful tools in geometrical designing of roof skeletons. Solving roofs with neighbors is much easier if we bring them to solve simple roofs over simpleconnected polygon base. The difficulty comes to the design of an appropriate polygonal base. This method essentially involves applying geometric design of a regular roof to design a roof with constraints, which can be relatively easily performed with a CAD program [13]. The elements of a roof: a) a roof with its elements in the orthographic projection, b) the roof with its elements in a military axonometry, c) the line of disappearing ridges of the roof in the orthographic projection [9].
regular roof skeleton, geometry of roof skeletons, roofs with neighbours, shape of roof.
The paper contains results of the next stage of research into the shape of roofs. Roofs are treated as a special class of polyhedral surfaces. The author proposes a new approach to so me problems of Descriptive Geometry concerning the geometry of roofs. The author presents a proposition of geometric design (geometric determination) of roofs with constraints, the so called «roofs with neighbours» and its influence to the teaching of Descriptive Geometry. The multi-surface roof with neighbours is spanned over such a polygon that a portion of the base does not belong to the line of eaves. In other words the line of eaves does not cover the base of the roof (Fig. 2, [16]; Fig. 3, [17]). The design involves the appropriate embedding of a roof with constraints in a roof over a simple-connected polygon, designing a regular roof and performing appropriate Boolean operations.
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