Customizing common parameters of logarithmic interpolation and Kriging

Customization of options of logarithmic interpolation, kriging and cokriging

Logarithmic interpolation, kriging and cokriging use identical algorithms of loading and search of points for construction of a local surface.

Direction of search for points to construct a local surface

Search of points to construct a local surface can be performed by sectors (4 or 8) or irrespective of a direction (by a circle). Search of points by sectors ensures location of a defined element within the local area. Outside of a polygon describing the reference points the surface continues a prevailing inclination of boundary points, therefore value of height can significantly differ from heights of reference points. For this reason, application of search by a circle is justified only if the reference points are located evenly, for example, in nodes of a regular network.

The number of points for constructing a local surface

If search of points is carried out by sectors, the number of points for constructing surface should be a multiple of the number of sectors for the average-weighted location of points in different directions. Increasing the number of points improves smoothness of a matrix, but slows down processing.

Number of updated points for conversion of a local surface

Calculation of the local surface is the most resource-intensive process in the construction of the matrix. For reducing the number of reorganisation iterations of a local surface it is possible to enter nonzero number of the updated points. In this case the surface will be reconstructed, when the number of new points for surface's construction will reach the specified limit.

Addition of points on border of linear and area objects

Algorithms of logarithmic interpolation, Kriging and Ccokriging can process only the point data. Therefore linear objects should be transformed to points. If the distance between the nodes of linear objects is large, then the following situation can arise. If the line goes near to a defined element, and line nodes are far from the line, the line will not be considered at calculation of a local surface. To solve this problem, at loading between nodes of linear objects the points are added by linear interpolation of nodes coordinates.

The size of a step into 1 element guarantees the considering the lines, which are going on distance to one element from the defined element. At a higher step a skipping the nearest lines are possible. Please be aware that decreasing the size of the step results in slower processing speeds due to the increase of the total number of points.

At irregular location of points logarithmic interpolation has the following feature: densely located points have a greater influence on a surface, that is especially appreciable in areas where change of density of points locations coincides with height difference. In these places distortions arises continuing the prevailing inclination of a surface in the area of a dense   points location.

For example, at constructing a matrix of heights by horizontals at transition from steep slopes which are described by the several closely located horizontals, to a valley where there is almost no horizontals, in valleys the deep pits are formed that continue the steep inclination of a surface on slopes. To solve this problem two modes are added:

Adding virtual points in empty regions with the specified step by a method of the average-weighted interpolation

The average-weighted interpolation is understood as a method of interpolation which is applied in an appropriate method (Kriging, cokriging or logarithmic interpolation), only at surface's construction the nearest points are used. Therefore, curvature of a local surface is not influenced by the considerable differences of heights of more distant points.

Enabling this mode for the example described above, leads to filling of valleys with plane, almost flat surface.

The step of adding points to empty regions is recommended to be set from 3 to 10 elements depending on density of points arrangement. Please be aware that decreasing the size of the step results in slower processing speeds due to the increase of the total number of points.

Do not give the height to go beyond the heights of neighboring points

At the enabled mode, for each local surface there are calculated limits on height for defined points (the minimum height of the nearest points minus the tolerance, the maximum height of the nearest points plus tolerance). If the calculated height of a defined element has gone beyond these limits, instead of the calculated value into a matrix the limiting value of a range is recorded.

Enabling this option will solve the problem of the appearance of the pits (hills) on border of transition of the surface's slope to the plain.

Additional parameter for cokriging

For cokriging it is necessary to choose semantics for the additional characteristic in standard dialog of semantics choice.