Because of the flexibility of free-form deformations, implementations must be careful to maintain properties of a surface that the designer would consider desirable. Most important is the smoothness of mesh being manipulated. If the mesh approximates a continuous surface, it should be approximately continous in its transformed state. Lattices have been used in the past to construct an exo-skeleton around the mesh to be manipulated. When the lattice is deformed, it deforms the space it encompasses.
Lattices are simple to construct and give a precise sense of their region of influence.
By moving the control points of a simple lattice, the designer can easily manipulate the complex unstructured mesh underneath. Unfortunately, lattice manipulations do not necessarily guarantee preservation of continuity. The lattice specified by the designer, for the sake of simplicity and intuition, is coarse and large-scale. This problem can be solved, however, by maintained subdivided versions of the lattice internally, and deforming the space in terms of these subdivided lattices. The subdivided lattices converge on a trivariate cubic B-spline, and thus are guaranteed to be smooth no matter what the deformation.