We have derived the Lagrangian equations of motion for D-NURBS. When
working with D-NURBS, a modeler may impose design requirements in
terms of energies, forces, and constraints. For instance, the modeler
may apply time-varying forces to sculpt shapes interactively or to
optimally approximate data. Certain aesthetic constraints such as
``fairness'' are expressible in terms of elastic energies that give
rise to specific stiffness matrices 
. By building the
physics-based D-NURBS generalization upon the standard NURBS geometry,
we allow the modeler to continue to use the whole spectrum of advanced
geometric design tools that have become prevalent, among them, the
imposition of geometric constraints that the final shape must satisfy.
For example, if the shapes of certain cross-sectional curves in a
NURBS surface must be circular arcs, the control points associated
with these curves must be constrained geometrically to admit only
circular arcs. Other constraints include the specification of
positions of surface points, the specification of surface normals at
surface points, and continuity requirements between adjacent surface
patches or curve arcs.