We present a pipeline of algorithms that decomposes a given polygon model into parts such that each part can be 3D printed with high (outer) surface quality. For this we exploit the fact that most 3D printing technologies have an anisotropic resolution and hence the surface smoothness varies significantly with the orientation of the surface. Our pipeline starts by segmenting the input surface into patches such that their normals can be aligned perpendicularly to the printing direction. A 3D Voronoi diagram is computed such that the intersections of the Voronoi cells with the surface approximate these surface patches. The intersections of the Voronoi cells with the input model's volume then provide an initial decomposition. We further present an algorithm to compute an assembly order for the parts and generate connectors between them. A post processing step further optimizes the seams between segments to improve the visual quality. We run our pipeline on a wide range of 3D models and experimentally evaluate the obtained improvements in terms of numerical, visual, and haptic quality.