A method for calculating a support material volume, the method comprising generating a grid of cells for a tree data structure of a digital part, where the cells define a plurality of cell arrays, and pinging the cells of one of the cell arrays until a cell containing a subset of the tree data structure is reached or until each cell in the cell array is pinged, where if a cell containing the subset of the tree data structure is reached, then designating the reached cell and all remaining unpinged cells in the cell array as filled. The method also includes repeating the pinging step for each remaining cell array to determine a total filled volume, and subtracting a volume of the digital part from the total filled volume to determine a support material volume.