In an illustrative implementation of this invention, a 3D object comprises substrate layers infiltrated by a hardened material. The 3D object is fabricated by a method comprising the following steps: Position powder on all or part of a substrate layer. Repeat this step for the remaining substrate layers. Transform the powder into a substance that flows and subsequently hardens into the hardened material. The hardened material solidifies in a spatial pattern that infiltrates positive regions in the substrate layers and does not infiltrate negative regions in the substrate layers.