Bezier introduced the idea of globally deforming a shape through a
mapping implemented as a free-form (tensor
product) spline. The shape is embedded in the spline and deformed by
manipulating the spline's control points. Sederberg and Parry
[30] popularized this concept of free-form deformation
(FFD) in the graphics literature.
We can arrive at a physics-based version of the FFD in which the object to be deformed is embedded in the D-NURBS ``material'' and deforms along with the deforming D-NURBS. The physics-based deformation is similar in motivation to the one devised in [7], but it offers fully continuous dynamics by virtue of the continuous nature of D-NURBS. In particular, we can apply forces at arbitrary points in the D-NURBS space to control the deformation directly (rather than through indirect manipulation via control points).