Direct manipulation of RDMS free form deformation

In this paper, we investigate the direct manipulation problem of free form deformation with rational DMS spline volume (RDMS-FFD). For the weights based direct manipulation method, the solution of the weights can be achieved by solving a linear system; for the control points based method, the explicit solution of displacements of the control points can be obtained, and some properties are also derived from the results. For the constraint points inside the control lattices, we use the weights based methods; for the constraint points outside the control lattices, the control points based method is adopted. Several examples are presented to show the effectiveness of the proposed methods.