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V Konferencja

Matematyka w naukach technicznych

i przyrodniczych

Krynica, 5-7 czerwca 2000


 

The Geometric Models of Roofing 

Kamil Maleček, Dagmar Szarková

Czech Technical University, Slovak Technical University

kamil@kmat.fsv.cvut.cz, szarkova@sjf.stuba.sk

 

 

Streszczenie

cesky

 

The paper has three parts, where  some surfaces are introduced. These surfaces are geometric models of roofing. We present a unified method for creating roofing of the ground view of a circle and a rectangle.

In the first part of the paper, we deal with the surfaces that are the geometric models for roofing of the ground view of the circle k in the plane pi. Surfaces are created with contour lines, which are obtained by the affine transformation of the circle k and by the translation defined by the vector perpendicular to the plane pi. We also introduce a mathematical description of these surfaces.

The second part of the paper contains a roofing for the ground view of a square or a rectangle by the pavilion, saddle or hip roofing. These classical roofs are created in the same way as the surfaces used for the roofing of the ground view of a circle.

In the third part of the paper, we present a roofing for the ground views of a rectangle and a circle by shells. Their geometric model is a segment of hyperbolic paraboloid. This part of the paper is accompanied with photos, which illustrate the roofing by shells of the St. Maria’s church in Prague-Strašnice.