Fabricable Eulerian Wires for 3D Shape Abstraction

摘要

We present a fully automatic method that finds a small number of machinefabricable wires with minimal overlap to reproduce a wire sculpture designas a 3D shape abstraction. Importantly, we consider non-planar wires, whichcan be fabricated by a wire bending machine, to enable efficient constructionof complex 3D sculptures that cannot be achieved by previous works. Wecall our wires Eulerian wires, since they are as Eulerian as possible withsmall overlap to form the target design together. Finding such Eulerian wiresis highly challenging, due to an enormous search space. After exploring avariety of optimization strategies, we formulate a population-based hybridmetaheuristic model, and design the join, bridge and split operators to refinethe solution wire sets in the population. We start the exploration of eachsolution wire set in a bottom-up manner, and adopt an adaptive simulatedannealing model to regulate the exploration. By further formulating a metamodel on top to optimize the cooling schedule, and precomputing fabricablesubwires, our method can efficiently find promising solutions with low wirecount and overlap in one to two minutes. We demonstrate the efficiency ofour method on a rich variety of wire sculptures, and physically fabricate severalof them. Our results show clear improvements over other optimizationalternatives in terms of solution quality, versatility, and scalability.