In a computer-implemented method for constructing a three-dimensional model of an object volume, cubic voxels cooperatively define a three-dimensional solid of the three-dimensional model of the object volume. Each voxel has a plurality of voxel faces, and each voxel face is parallel to one of three axes of a rectangular coordinate system. Each voxel has a data structure that includes an object flag portion for describing the corresponding three-dimensional solid, a face flag portion for indicating which ones of the voxel faces serve as a boundary face of the corresponding three-dimensional solid, and a set of distance-levels that represent sample points of the voxel on the three axes of the rectangular coordinate system. The topology and geometry of a boundary of the three-dimensional solid are represented by the face flag portions and the distance-levels of the voxels that are positioned at the boundary.