Printable Aggregate Elements.

Aggregating base elements into rigid objects such as furniture or sculptures is a great way for designers to convey a specific look and feel. Unfortunately, there is no existing solution to help model structurally sound aggregates. The challenges stem from the fact that the final shape and its structural properties emerge from the arrangements of the elements, whose sizes are large so that they remain easily identifiable. Therefore there is a very tight coupling between the object shape, structural properties, and the precise layout of the elements. We present the first method to create aggregates of elements that are structurally sound and can be manufactured on 3D printers. Rather than having to assemble an aggregate shape by painstakingly positioning elements one by one, users of our method only have to describe the structural purpose of the desired object. This is done by specifying a set of external forces and attachment points. The algorithm then automatically optimizes a layout of user-provided elements that answers the specified scenario. The elements can have arbitrary shapes: convex, concave, elongated, and can be allowed to deform. Our approach creates connections between elements through small overlaps preserving their appearance, while optimizing for the global rigidity of the resulting aggregate. We formulate a topology optimization problem whose design variables are the positions and orientations of individual elements. Global rigidity is maximized through a dedicated gradient descent scheme. Due to the challenging setting -- number of elements, arbitrary shapes, orientation, and constraints in 3D -- we propose several novel steps to achieve convergence.