Abstract: The present invention provides a meshing method, called grafting, that lifts the prior art constraint on abutting surfaces, including surfaces that are linking, source/target, or other types of surfaces of the trunk volume. The grafting method locally modifies the structured mesh of the linking surfaces allowing the mesh to conform to additional surface features. Thus, the grafting method can provide a transition between multiple sweep directions extending sweeping algorithms to 2¾-D solids. The method is also suitable for use with non-sweepable volumes; the method provides a transition between meshes generated by methods other than sweeping as well.