Selects a minimal set of points so that each point from the source set is within the given distance to at least one point of the result set. The distance is given in the drawing's native measurement units.
This is a very useful operator when locating antennas for some types of wireless services.
Example
Suppose we have a network created from roads in a town. The drawing is in Orthographic projection, which by default uses meters as the projection unit.
A point has been placed at the end of each line using the Points operator. Duplicate points have been removed with the Remove Duplicates operator. We could now delete the roads, since we no longer need them, but we will keep them for display purposes.
We can run the Select Euclidean Point Coverage operator in the transform toolbar on all objects using a parameter of 500. Because the drawing uses meters in its projection coordinate system, we are asking Manifold to construct the Euclidean point coverage using a distance of 500 meters.
The result of the operator is that four points have been selected and shown in red selection color.
If we draw circles about each red point that are 500 meters in radius, we can see that Manifold has selected four points such that every other point in the network lies within 500 meters of one of the four points.
The point coverage selected is minimal, because no fewer than four points can be selected such that all other points are within 500 meters of a selected point. We cannot choose only three points, for example, within 500 meters of all the other points. Four points are minimal, because five points are not necessary.
The point coverage is said to be Euclidean because the distances between points that are measured to be 500 meters or less are computed using straight line, Euclidean distance. They are not distances as measured through the network.
Note that the point coverage selected by Manifold is not guaranteed unique. There may be a different set of four points that also covers the other points to a distance of 500 meters. The guarantee is simply that there is no set of three or fewer points that is also a coverage to 500 meters of this particular network, and that the selected set of four points is a coverage to 500 meters.
Note that the illustration suggests a practical usage for this operator. Suppose we have a road network within a region that we would like to saturate with wireless service, such as wireless communications between centralized polling stations and reporting nodes. If each wireless antenna can cover a 500 meter radius and we would like to locate antennas only at nodes (to take advantage of the ease of trenching roads or pulling cable through existing conduits) we can use the Select Euclidean Point Coverage operator to find possible coverages with the minimal number of antennas required.
Units of Measurement
Units used for the distance value in the source / argument box are taken from the projection of the drawing. If the drawing is in Latitude / Longitude projection the units will be degrees. If the drawing is projected, the units will be in meters or feet. It is therefore strongly recommended that the drawing be projected first so that meters or other linear measure can be used instead of attempting to use degrees as a measurement unit.
To see which units are defined for the drawing's projection, click on the Tracker tool and make some measurements. Whatever units are used to show the result of the tracker tool are the units currently in force.
If the drawing uses degrees and meter-based creation of buffer zones are desired, first re-project the drawing into any convenient meter-based projection (such as Orthographic) so that meters will be used as the units of measure.
When this transform operator is used with a drawing layer within a map the units used by the drawing will be used. If the map component's projection is degree based while the native projection for the drawing is meter based (as, for example, with the Orthographic projection) or vice versa, then the transform operator will use whatever units are used by the drawing's projection.
See Also