A method for creating three dimensional lattice structures in computer-aided design models, said method being a computer-implemented method, said method comprising: receiving a solid model containing a plurality of boundary surfaces for a void region; computing a bounding box of the solid model and a plurality of grid points on an axis-aligned grid forming a lattice grid within the bounding box; creating a lattice cell layout for a lattice structure within the void region; computing an implicit model defined by a scalar value for each of the grid points on the axis-aligned grid, wherein the scalar value for each grid point is determined by: calculating a surface distance based on a minimum distance for the grid point to the boundary surfaces; calculating a lattice distance based on the minimum distance for the grid point to the lattice structure; and setting the scalar value based on a lesser of the surface distance and the lattice distance; and extracting the lattice structure in the solid model based on the implicit model, wherein a cell template is specified for application within the solid lattice model, and wherein a cell template shape is designed as a skeleton structured of connected line segments and an associated thickness that defines the 3D volume of the template as an offset of the skeleton; storing the lattice structure in the solid model based on the implicit model, and combining with the outer surface of the solid model to fabricate the desired model with lattice structures, and manufacturing the extracted lattice structure, wherein the lattice structure is a 3D lattice structure for supporting a hollow object in additive manufacturing. receiving a solid model containing a plurality of boundary surfaces for a void region; computing a bounding box of the solid model and a plurality of grid points on an axis-aligned grid forming a lattice grid within the bounding box; creating a lattice cell layout for a lattice structure within the void region; computing an implicit model defined by a scalar value for each of the grid points on the axis-aligned grid, wherein the scalar value for each grid point is determined by: calculating a surface distance based on a minimum distance for the grid point to the boundary surfaces; calculating a lattice distance based on the minimum distance for the grid point to the lattice structure; and setting the scalar value based on a lesser of the surface distance and the lattice distance; and calculating a surface distance based on a minimum distance for the grid point to the boundary surfaces; calculating a lattice distance based on the minimum distance for the grid point to the lattice structure; and setting the scalar value based on a lesser of the surface distance and the lattice distance; and extracting the lattice structure in the solid model based on the implicit model, wherein a cell template is specified for application within the solid lattice model, and wherein a cell template shape is designed as a skeleton structured of connected line segments and an associated thickness that defines the 3D volume of the template as an offset of the skeleton; storing the lattice structure in the solid model based on the implicit model, and combining with the outer surface of the solid model to fabricate the desired model with lattice structures, and manufacturing the extracted lattice structure, wherein the lattice structure is a 3D lattice structure for supporting a hollow object in additive manufacturing.