Pylypaka S. Construction of surfaces and their continuous winding in finite forms on the base of operation of the natural parameters

Thesis is devoted to the working out of new direction in surface construction and their continuous winding in finite forms in the base of natural parameters usage. Proposed kinematic approach in the construction of curve lines on given equations of curvature and forsion is the base of investigations. The construction of surface is carried out in the system of accompanying three - edge of received curve. The kind of surface depends on derivative curve, fixed in three - edge The models of continuous winding of lined surfaces and some unlined ones (curved surfaces of Monge, surfaces of transfer, screw were created on the base of invariability of coefficients of the first quadratic form. Geometrical essence of winding process was proved. Obtained results were grounded theoretically and confirmed by the installations in production and educational process.