The present disclosure provides various three-dimensional (3D) objects, some of which comprise a wire or 3D plane. Disclosed herein are methods, apparatus, software, and systems for their generation that may reduce or eliminate the need for auxiliary support during the formation of the 3D objects. The methods, apparatuses, software, and systems of the present disclosure may allow the formation of objects with short, diminished number, and/or spaced apart auxiliary support structures. These 3D objects may be objects with adjacent surfaces such as hanging structures and planar hollow 3D objects.