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When performing an overlay or intersect I would like to know if there is a way to ignore selection when intersection or overlay is less than a certain percentage of area or less than a certain number of crossing map units of the perimeter of a polygon.

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The "Select Within" plugin will allow you to do mostly within selections.

So you can supply a % number. So you can select all of the features from a layer that are at least 50% within the selecting layer.

Check out:

https://gisforthought.com/qgis-select-within-plugin-0-4/

https://plugins.qgis.org/plugins/SelectWithin/

So you could run that, and create a selection, then run the overlay or intersection using only the selected features.

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