Boyko L. Approximation of screw conoid and catenoid by compartments of the same type of unfold surfaces

The approximation is carried out along the lines, set in interior curvilinear co-ordinates of initial surface. The approximating surface is as bending one of the one-parametre multitude of the planes, tangential to the initial surface along the line set. Different curves, including such special ones, as asymptotic, geodesic and curvature lines, were taken for line of contact. It has been obtained parametric equations of the approximating surface, its ribs of turn and ivolvent. The approximation along the lines of conoid curvature is the best. The compartment of the approximating surface restricted by lines of intersection with coaxial cylinders and contiguous compartments has been discovered. A plane blank with lines of a pattern for its bending into the necessary surface compartment has been built. The approximation of screw conoid is carried out by the multitude of the compartments of the same type.