incremental vector , i.e. where - is the number of interior node of the area, - the number of co-ordinate After all transformations we may write the following two independent systems of linear algebraic equations where - symmetrical matrix in the banded form similar to global stiffness matrix of FEM assemblage, and - incremental vectors of co-ordinates of all nodes at axes 1, 2, and - the right part vectors that are combined by co-ordinates of all nodes in axes 1, 2. The solution of both systems, keeping all boundary nodes conservative, obtains new interior node positions corresponding to a non-distorted mesh with pseudo-regular elements. For example, Fig. 2 presents the rectangular area covered by a triangular mesh. The initial auto mesh possesses some degenerative triangles (left mesh). The final mesh (right mesh) produced by the SGM procedure is pseudo-regular without any distorted elements. As above systems are linear, the procedure elapses very quickly to a one-step solution. Moreover, each final interior node position meets the requirement of co-ordinate arithmetic mean of nodes surrounding it and meets the Delaunay criteria too. Therefore, the SGM has all the positive values peculiar to Laplacian and other kinds of smoothing approaches but much easier and reliable because of integer-valued final matrices representation. Finally, the described above SGM is perfectly applicable not only to 2D meshes but to 3D meshes consisting of any uniform cells as well as to mixed or transient meshes. Minimum surface problem solution Mathematically the surface embedded into a non-plane closed curve is called minimum if its area is minimal amongst all the surfaces passing through this curve. The best-known minimum surface sample is a soap film bounded by wire frame. Usually to create a minimum surface, a fictitious constitutive law, which maintains a constant prestress, independent of any changes in strain, is used. The alternative approximated approach to the minimum surface problem solution is based on SGM. This formulation allows one to minimize the surface embedded into non-plane and plane closed contours. The idea is to approximate a surface part embedded into 3D non-plane contour by an arbitrary triangle grid. To converge such triangle grid to grid with minimum area one should solve the same two systems described above. Increments of the third nodal co-ordinates may be determined additionally by similar system at axis 3 in the following way Solving all three systems simultaneously one can obtain a new