We propose a method for the automatic segmentation of 3D objects into parts which can be individually 3D printed and then reassembled by preserving the visual quality of the final object. Our technique focuses on minimizing the surface affected by supports, decomposing the object into multiple parts whose printing orientation is automatically chosen. The segmentation reduces the visual impact on the fabricated model producing non‐planar cuts that adapt to the object shape. This is performed by solving an optimization problem that balances the effects of supports and cuts, while trying to place both in occluded regions of the object surface. To assess the practical impact of the solution, we show a number of segmented, 3D printed and reassembled objects.