Three-dimensional printing of three-dimensional objects

A three-dimensional object, comprising:

• a plurality of layers of hard material stacked layerwise and bonded together to form a shape of the three-dimensional object, wherein a layer of the plurality of layers defines a layering plane, which plurality of layers comprises:
• a first section comprising a first microstructure associated with being formed at a first solidification rate;
• and
• a second section is at least a portion of an overhang comprising:
• (i) a second microstructure associated with being formed at a second solidification rate that is different from the first solidification rate, and (ii) an exterior surface corresponding to at least a fraction of an exterior surface of the three-dimensional object,
• wherein an overhang vector at a point on the exterior surface of the second section is normal to a surface at the point in a direction towards an interior of the overhang,
• wherein a stacking vector corresponds to a stacking direction of the plurality of layers, which stacking vector is normal to the layering plane,
• wherein the overhang vector has a positive projection onto the stacking vector,
• wherein the stacking direction of the plurality of layers is determined from (1) a direction of expansion of a melt pool that is included in the plurality of layers, (2) a direction opposite from a first surface comprising an auxiliary support or auxiliary support mark, (3) a direction towards a second surface comprising hatch marking, (4) a direction towards a smoother surface of two opposing surfaces, and/or (5) a directionality in grain orientation indicative of print orientation.