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Obsolete description follows.

This is an enhanced and customizable version of the sieve by pcstru.
Enter Customizer to create a model with your own desired specifications.
If Customizer is broken on the Thingiverse website, here are instructions to run it on your own computer.

This updated version allows to choose between round or square shapes, or you can make any regular polygon shape by reducing the number of circle segments. The polygon will fit inside a circle of the specified outer diameter (this means making a 4-sided polygon is not the same as selecting the ‘square’ shape).
Another tweak creates the model such that the grid should be well-attached to the rim even when using few or thin strands, and my unstoppable urge for detail made me ensure that the grid is perfectly centered at all times.

You can opt to print the grid as one set of layers, i.e. a plane with holes in it, or to print two sets of strands on top of each other (‘offset’ option). The latter is easier and probably faster to print, and may yield a more accurate filter if hole size is important. The disadvantage is that dirt tends to stick to the filter more easily.

You can also opt to lift the grid. This allows to print accurate filters with strands merely as wide as your nozzle diameter (see photos). Set the lift distance to your first layer height to ensure the filter only starts being printed at the second layer. This avoids that the strands get squished against the bed, or printed with a wider first layer extrusion, both of which would make the hole size inaccurate. You could also use a raft to the same effect, but it might be difficult to remove the filter form the raft without damaging it.