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In OpenJump there is a tool called ClosedVertexFinder which you can use to find vertices which are too close to each other.

https://github.com/ssinger/roadmatcher/blob/master/src/com/vividsolutions/jcs/qa/CloseVertexFinder.java

I would like to build a tool like this in QGIS.

Is there something that can already be used in order not to build the tool from scratch or will I have to calculate the distance between all vertices of a layer?

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