Construct a triangulation by marked pickets

The purpose of construction of a triangulation is the join of the pickets selected on a map into a network of noncrossed triangles, satisfying to conditions of the Delone theorem.  

Delone triangulation is a partitioning of irregular set of reference points onto such network of triangles which would satisfied the Delone theorem formulated still in the thirtieth years about an empty sphere. In the application to bidimentional space it is formulated as follows: the system of the interconnected noncrossed triangles has the least perimeter if any of tops does not get inside of any of the circles described around of formed triangles. It means, that the formed triangles at such triangulation as much as possible approximate to equilateral triangles, and each of the sides of the formed triangles from opposite top is visible under the maximal angle from all possible points of the corresponding half-plane. It is that optimum triangulation by which edges linear interpolation for construction of isolines is done (variants of nonlinear interpolation on the same basis are possible).  

The constructed triangulation is the initial information for construction of sections of the future isolines. In existing technology of construction of isolines, for more exact construction of sections, there is an opportunity to carry out a thickening or decomposition of a triangulation. Into the center of each triangle, satisfying to a control ratio of the area and perimeter, artificially the point is added. Values of coordinates and semantics of a point are defined by the equation of a plane. The triangulation is reconstructed and already by the changed triangulation the construction of sections is carried out.