This document describes techniques and apparatuses for 3D printing with small geometric offsets to affect surface characteristics. These techniques are capable of enabling fused-deposition printers to create 3D objects having desired surface characteristics, such as particular colors, images and image resolutions, textures, and luminosities. In some cases, the techniques do so using a single filament head with a single filament material. In some other cases, the techniques do so using multiple heads each with different filaments, though the techniques can forgo many switches between these heads. Each printing layer may use even a single filament from one head, thereby enabling surface characteristics while reducing starts and stops for filaments heads, which enables fewer artifacts or increases printing speed.