The proposed method of specifying the surface of a particular discrete frame with a flat 3-tissue. A one-parameter non-parametrized family of curves is given, i.e. a discrete frame of lines. There are two cases of specifying the lines of a discrete surface frame: point series or equations. In the article the questions of the task spatial 3-a fabric flat. In this case, the basic concepts of a proper tetrahedron and a complete quadrilateral are used. If the fabric M has two families of diagonal surfaces, then it also has a third similar family.

Keywords: descriptive geometry, graphics, octahedral 3-tissue, spatial 3-tissue, full quadrilateral, topology, affine geometry, regular 3-tissue, projective geometry, involution

We will call the Geometrical Determinant (GD) set of geometrical elements which define a fabric task 3 for the planes. GO curvilinear 3 fabrics can be only in various way organized 3 families of curves. Rectilinear 3 fabric can be set by various GO.

Keywords: Flat 3 fabric, geometrical determinants, curvilinear 3 fabric, rectilinear 3 fabric

The way of a task of a surface certain by a discrete framework by means of flat 3 fabrics is offered. The one-parametrical not parametrized family of curves, i.e. a discrete framework of lines is set. Two cases of a task of lines of a discrete framework of a surface are possible: dot ranks or equations

Keywords: Discrete, framework, surface, flat, 3 fabric, spline, equations, 3 fabrics, surfaces

Article is devoted to designing of surfaces on the basis of flat 3-fabrics.Such families 3 of lines which block some area of the plane so are called as flat 3 fabric that through each point of this plane passes 3 lines of different families. Functional determinants of this of 3 fabrics anywhere in area doesn't address in zero, two curves of various families have no more than one general point. 3-fabric used in our case is the hexagonal, i.e. consisting of families parallel straight lines. Each line of 3 families bears on itself information on parameters of lines of the modelled surface. On the basis of information which is born on itself by each straight line of three families, some surface is modelled.

Keywords: designing of modeling, computer graphics, modeling of surfaces,hexagonal 3-fabrics

Article is devoted to a subject: in space some closed curve is set; among all possible surfaces passing through this curve to find such for which the part it concluded in a curve would have the smallest area. Curvature of any curve on a surface is equal in the set its point to curvature of flat section of a surface the adjoining curve plane.

Keywords: minimum surfaces, modeling, 3 fabric, curvature of a surface, equation of average curvature