Transform: Center and Centroids

Three related Transform dialog templates, called Center, Center, Inner and Center, Weight, create points at the "center" of objects using similar but different methods.    These templates are listed in the Transform Templates - Geom



Such points are often called centroids in GIS work.   The word centroid in this context simply means a point placed at the "center" of an object.   Centroids are used for many reasons but perhaps the most important is to convert geographic data in the form of areas or lines into the simpler form of points. At times we will want the data in a simpler form for export to other programs or to use analytic methods that work with points but which do not work with areas or lines.



sc_centroids_01.png  sc_centroids_02.png



A point is always its own centroid, so the Center template simply copies points. The Center template can work with lines as well as with areas. When a centroid point is created it inherits the data fields of the object from which it was created. The illustrations above show centroids created for areas with the Centers template.



The Center, Weight template creates a point at the approximate center of balance of the area, that is, the balance point if the area were cut out of stiff cardboard.   The centroid point created by the Center, Weight template is shown above in yellow.  The Center, Weight template uses a fast algorithm that will usually, but not always, place the centroid point within the area. Unusual area shapes such as horseshoe shapes will cause the centroid point to be placed outside the area.




The Center template computes a minimum enclosing circle about each area and creates the centroid at the center of the circle. The illustration above shows the centroid point created by the Centers template in red.  The position of the Center  centroid is different from the centroid computed by the Center, Weight template.


Center, Inner


We will often encounter areas where the centroid point computed using Center or Center, Weight will be placed outside the area.   Consider, for example,  a map of the Southeastern United States.




If we create centroids, shown as green dots, using the Centers template we see that the centroid for Florida falls outside of the state.




If we were too zoom far into the drawing we would see that the centroid created for Louisiana also falls outside that state, just across the border within Mississippi.




We can use the Center, Inner template to create centroids, shown as yellow squares above, that are guaranteed to fall within their areas.


Centers and Lines


Because an enclosing circle can be computed for lines as well as for areas we can create centroids for lines using the Center template.





This illustration shows four lines with their centroids, computed using Center.



If we draw enclosing circles about each line, shown in red selection color, we can see how the locations of the centroids were determined.


Centers are most frequently created for areas. However, they are also a useful means of "converting" line objects into point data.




For example, the above illustration shows lines in a hydrography layer where what appear to be continuous lines are in fact many lines that abut one another.




Using the Center template we can create centroids for each individual line.


Why would we want to do that?  Suppose for each line segment we have the length of the line. We would like to know the total length of waterways per square kilometer in various regions of the map. We can approximate this by creating a grid where each box is one kilometer square and then creating centroids for each line segment. It is then an easy matter to add up the total "length" values for each centroid point that happens to be in each square kilometer grid box.



See Also

Transform Dialog


Transform Options


Transform Templates


Transform Templates - Geom