Construction of triangulation

The purpose of construction of a triangulation is association of pickets into a network of the triangles, satisfying to conditions of Delone theorem.

Delone triangulation is a splitting of irregular set of control points into such network of triangles which would respond the Delone theorem formulated already in the thirtieth years about an empty sphere. In the application to bidimensional space it is formulated as follows: the system of the interconnected not overlapped triangles has the least perimeter if any of apices 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 triangle, and each of the sides of the formed triangles from opposite apex is visible under the maximal corner from all possible points corresponding to a half-plane. It is that optimum triangulation by edges of which the linear interpolation for construction of isolines is made (variants of and 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 condensation additionally 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 on the equation of a plane. The triangulation is reconstructed and already on the changed triangulation the construction of sections is carried out.