Embodiments disclosed herein provide systems and methods for preparing geometry for 3D printing. In one embodiment, a 3D printing preparation application receives 3D geometry and repairs non-manifold edges and non-manifold vertices, producing a topological manifold geometry. The 3D printing preparation application then welds coincident edges without coincident faces and fills holes in the geometry. The 3D printing preparation application may further perform resolution-aware thickening of the geometry by estimating distances to a medial axis based on distances to distance field shocks, and advecting the distance field using a velocity field. A similar approach may be used to perform resolution-aware separation enforcement. Alternatively, one component may be globally thickened and subtracted from another for separation enforcement. The 3D printing preparation application may also split large models and add connectors for connecting the split pieces after printing. In addition, the 3D printing preparation application may generate a 3D print preview.