A method for printing a 3D structure comprising a 3D part and an associated support structure using an additive manufacturing system, the method comprising: using a computer for: for each slice of a three-dimensional build space; for each of a collection of voxels in said slice: selecting a voxel in the collection; for the selected voxel, determining, by a graphics processing unit, a distance field value relative to a digital part model in the three-dimensional build space, said distance field value being a length of a shortest vector between the selected voxel and mesh boundaries of the digital part model, wherein said determining comprises using the values in z-buffers of the graphics processing unit to determine distances from the selected voxel to a plurality of locations on the digital part model, and using the shortest distance to determine the distance field value, said values in z-buffers containing, for each voxel of the slice, a magnitude of a vertical distance between the voxel and the closest mesh boundary of the part; using the distance field value to select at least one material selection rule; applying the distance field value to the at least one material selection rule to identify (118, 906) a material designation for the selected voxel, wherein the material designation indicates no material is to be placed at the selected voxel when the material selection rule identifies no material for the selected voxel and wherein the material designation indicates at least one material is to be placed at the selected voxel when the at least one material selection rule identifies the at least one material for the selected voxel; and outputting the material designations for the collection of voxels in said slice; and using the additive manufacturing system to: print the 3D part and associated support structure using the output material designations for the collection of voxels. for each slice of a three-dimensional build space; for each of a collection of voxels in said slice: selecting a voxel in the collection; for the selected voxel, determining, by a graphics processing unit, a distance field value relative to a digital part model in the three-dimensional build space, said distance field value being a length of a shortest vector between the selected voxel and mesh boundaries of the digital part model, wherein said determining comprises using the values in z-buffers of the graphics processing unit to determine distances from the selected voxel to a plurality of locations on the digital part model, and using the shortest distance to determine the distance field value, said values in z-buffers containing, for each voxel of the slice, a magnitude of a vertical distance between the voxel and the closest mesh boundary of the part; using the distance field value to select at least one material selection rule; applying the distance field value to the at least one material selection rule to identify (118, 906) a material designation for the selected voxel, wherein the material designation indicates no material is to be placed at the selected voxel when the material selection rule identifies no material for the selected voxel and wherein the material designation indicates at least one material is to be placed at the selected voxel when the at least one material selection rule identifies the at least one material for the selected voxel; and outputting the material designations for the collection of voxels in said slice; and using the additive manufacturing system to: print the 3D part and associated support structure using the output material designations for the collection of voxels. selecting a voxel in the collection; for the selected voxel, determining, by a graphics processing unit, a distance field value relative to a digital part model in the three-dimensional build space, said distance field value being a length of a shortest vector between the selected voxel and mesh boundaries of the digital part model, wherein said determining comprises using the values in z-buffers of the graphics processing unit to determine distances from the selected voxel to a plurality of locations on the digital part model, and using the shortest distance to determine the distance field value, said values in z-buffers containing, for each voxel of the slice, a magnitude of a vertical distance between the voxel and the closest mesh boundary of the part; using the distance field value to select at least one material selection rule; applying the distance field value to the at least one material selection rule to identify (118, 906) a material designation for the selected voxel, wherein the material designation indicates no material is to be placed at the selected voxel when the material selection rule identifies no material for the selected voxel and wherein the material designation indicates at least one material is to be placed at the selected voxel when the at least one material selection rule identifies the at least one material for the selected voxel; and outputting the material designations for the collection of voxels in said slice; and using the additive manufacturing system to: print the 3D part and associated support structure using the output material designations for the collection of voxels.