ANALYSIS OF THE SURFACE FORMS WITH A FRAMEWORK FROM THREE SUPERELLIPSES IN THE MAIN COORDINATE PLANES

Designers used rather often free form surfaces for the approximation of real products and bodies. These free form surfaces contain a given in advance main framework from several plane or space curves. Algebraical surfaces with given in advance main framework from three plane curves lying in the main coordinate planes are concerned with the particular place in technical design. A whole file of threes of surfaces of plane-and-parallel translation of superel-lipses of variable curvature of velaroidal type can be defined and described by the three algebraical equations if superellipses are taken as three plane curves of the main framework. Taking every of three superellipses by turns as a generatrix curve of variable curvature, one can design three different surfaces with the same main framework. First, it was elucidated that only one or two surfaces instead of three surfaces under appointed geometrical conditions one can construct for chosen exponents of powers in the formulae of superellipses of the main framework. It was shown that a three of surfaces contains surfaces of negative, zero, and positive gaussian curvatures in some appointed conditions, in particular, cylindroids, spheres, cones, cylinders, and surfaces of revolution.