Paint Reduce Weights works in conjunction with the Mesh > Reduce feature to let you reduce the number of polygons in a mesh while attempting to retain the shape of the original. The Paint Reduce Weights Tool lets you paint on the mesh to specify a region on the mesh where you want the polygons to be reduced.
You do this by first selecting the polygon mesh, and then selecting Mesh > Reduce > 
. Turn on the Keep Original option and then click Reduce. You then paint on the original mesh and a copy of the mesh is reduced.
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