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Is there a mechanism in blender similar to the solidify modifier that would allow me to apply thickness to a series of faces but have this thickness increasing or dropping off in certain places?

For example, the brim of a hat where I apply more thickness\weight in the center and less at the edges, or a cloak where I thin it down where there are creases and a standard solidify modifier can't handle them and starts overlapping itself.

My intention is to 3D print my models so controlling the thickness is important, and a pain to do manually.

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    $\begingroup$ You can choose a vertex group in the Solidify modifier, the thickness will depend on the weight of the vertices $\endgroup$
    – moonboots
    Sep 5 at 20:22
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Like moonboots said, you can use vertex groups and weight painting to change the thickness:

  1. Add a vertex group (Select your object, go to the green upside down triangle next to the materials tab and click on the plus icon)
  2. Select the modifier properties tab (the wrench near the yellow square) and add the solidify modifier from the add modifier dropdown
  3. Switch to weight painting either by holding down tab or choosing 'weight paint' on the drop down in the top left (it should say object mode by default)
  4. Paint like you would in sculpt or texture mode, bluer means the value of the area is closer to 0 and redder means it's closer to 1

You can optionally turn on the vertex group invert and mess with the factor slider to see what you prefer

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