A system for generating slice data for additive manufacturing, comprises a graphics processing unit (GPU) that receives a digital model of an object in a three-dimensional build space defined over a plurality of slices, computes a three-dimensional signed distance field over voxels in the build space, assigns a building material to each voxel based on a respective distance field value, and generates slice data output pertaining to the building material assignments for each slice. The slice data output can be used for printing the object in layers corresponding to the slices. The distance field comprises one or more vector having a vertical component with respect to the slices.