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Is it possible to reconstruct a grid of polygones or polylines from the centroids?

I am looking for a arcGIS tool or script that will allow me to reconstruct a grid of polygons or polylines from their centroids.

From centroids

to polygons

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up vote 2 down vote accepted

Voronoi polygons might work but you definitely don't want Delaunay triangulation for this task. However, if you know the grid to be regular, you can just use the Create Fishnet tool from the Data Management Tool box (under Feature Class tools). The Fishnet tool has a lot of options that with a little understanding of your point dataset, will enable you to recreate the grid easily.

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You can create Voronoids with ArcGIS with a ArcInfo license:

Voronoi diagram and Delaunay triangulation

To create a grid I'm not sure however. In theory any grid-creation tool should be able to do it because you don't actually need the points as they're uniform. If you know the distances between the points it should be easy to just enter the correct settings into a grid-creator tool and have it generate a grid that will be fit for purpose. ET GeoWizards has such a tool (Vector Grid) but there are probably free ones out there too.

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