The solution to the problem is supports, temporary parts of the model for printing which are removed after the print is finished. Most printers even have software to automatically create such supports. Unfortunately for my particular printer, the XYZ Da Vinci jr. 1.0w, the automatically created supports don’t work very well. The software simply creates supports straight up from the bottom under every minor overhang. That creates far more supports than actually needed, wasting material and producing lots of ugly connection spots on the underside of the model.
For some time I created supports manually, using Tinkercad. That is somewhat fiddly, and also far from optimized. Again the supports I design are mostly straight up from the bottom. Choosing the right number of support points is somewhat hit and miss, so sometimes I print a model, see where my design didn’t really cover an overhang, and then have to add more supports.
But recently I found a much better solution. The free Autodesk Meshmixer software has the possibility to generate supports in the Analysis – Overhangs menu. There are even tons of parameters you can set to optimize those supports. And instead of simple straight up supports, the software produces angled and branched supports, which use much less material. You can also optimize the thickness of the support and the width of the tip to create supports that are stable to print but minimize the size of the connection points.
This software has quite opened up my possibilities of printing miniatures for my game. For example the Princes of the Apocalypse cover art shows a winged female with a spear. Between the wings and the spear she would have been nearly impossible for me to print. But now I printed her with the Meshmixer generated supports and even managed to make her “fly”, her feet not touching the ground. Now I’m only limited by the fragility of the wings and spear when printed at 1:60 scale.