DESIGN OF UMBRELLA SURFACES FROM THE PARTS OF TRANSLATIONAL SURFACES FORMED BY THE CIRCLE OF CONSTANT RADIUS

The geometrical research of translational surface formed by the circle of constant radius supported by two meridians of the sphere or the torus is presented.
The vector equations are derived in lines of translation and in lines two of which coincide with the given meridians. The opportunity of design of umbrella shells is illustrated by the example of the real building.
The umbrella surfaces of positive and negative Gauss curvatures are presented.

sphere, translational surface formed by the circle of constant radius, a meridian on the sphere, a vector equation of the surface, umbrella surfaces of positive and negative Gauss curvatures