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Can Any Model Be Fabricated? Inverse Operation Based Planning for Hybrid Additive–Subtractive Manufacturing
DescriptionThis paper presents a method for computing interleaved additive and subtractive manufacturing operations to fabricate models of arbitrary shapes. We formulate the manufacturing planning problem by constructing a sequence of inverse operations that progressively transform a target model into a null shape. Each inverse operation corresponds to either an additive or subtractive step, ensuring both manufacturability and structural stability of intermediate shapes throughout the process. We theoretically prove that any model can be fabricated exactly using a sequence generated by our approach. To demonstrate the effectiveness of this method, we adopt a voxel-based implementation and develop a scalable algorithm designed to reduce overall manufacturing time. Our approach has been tested across a range of digital models and further validated through physical fabrication on a hybrid manufacturing system with automatic tool switching.