Embodiments of the invention provide systems and methods for nesting objects in 2D sheets and 3D volumes. In one embodiment, a nesting application simplifies the shapes of parts and performs a rigid body simulation of the parts dropping into a 2D sheet or 3D volume. In the rigid body simulation, parts begin from random initial positions on one or more sides and drop under the force of gravity into the 2D sheet or 3D volume until coming into contact with another part, a boundary, or the origin of the gravity. The parts may be dropped according to a particular order, such as alternating large and small parts. Further, the simulation may be translation- and/or position-only, meaning the parts do not rotate and/or do not have momentum, respectively. Tighter packing may be achieved by incorporating user inputs and simulating jittering of the parts using random forces.