Designing of Architectural Shells on the Basis of Linear Hyperbolic Congruence Surfaces

The possibilities of using the ruled surfaces of hyperbolic congruence for designing of architectural shells are considered in the article. The constructive design of selecting the surface from the hyperbolic congruence of straight lines with two proper directrices is given. In the general form, the extreme values of the distribution functions of the points on the directrices of congruences and conditions for the existence of torso generators on the surface are determined depending on the surface internal parameters. The dependence of the curvature radius of the principal non-zero direction along the torso generator on the position parameter of the point on the congruence ray is determined. The asymptotic lines for it are indicated. Specific examples show the solution of the inverse problems of applied geometry related to the determination of internal parameters of the surface depending on the given characteristics of the future shell: position-metric and differential problems.