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I have a vector file containing thousands of points. Where points are within x distance from each other, I wish to delete one of the points and keep the other (either by snapping to one point, or simply erasing one of the two points)

However, in Whitebox the vector cleaning tool only works with polygons and lines.

Is there some other way I can do this with my shapefiles?

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I followed Curlew's suggestion:

have a look at this tutorial:http://qgis.spatialthoughts.com/2013/04/tutorial-nearest-neighbor-analysis.html Compute the NN for each point, join and then delete all points below a threshold.

and computed the nearest neighbour analysis, joining the table to layer. Then simply exported to excel, sorted and selected by distance and then deleted duplicates via Data>delete duplicates!

Update: The latest tutorial is now at http://www.qgistutorials.com/en/docs/nearest_neighbor_analysis.html

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