INVARIANT ALGORITHMS OF SPATIAL CONSTRUCTIONS ELEMENTS FORMING AND CUTTING

This report clearly demonstrates the capabilities of an advanced research area of applied mathematics, i.e., computational geometry to be applied for shaping dimensional structures. Vector-matrix models are provided to cover the composite membrane piecewise-smooth structures composed of surface elements with zero Gaussian curvature. General algorithms are presented for finding cutting lines for cylindrically and conically-shaped elements, into which the curves contained in the developable surfaces transform. A dome-like peak-shaped structure comprising components of both cylindrical and conical shape is given as an example to present equations describing the cutting lines explicitly, which makes it possible to implement a high-precision technique for producing such a structure.