In the D-NURBS design scenario, sculpting tools may be implemented as
applied forces. The force 
in the D-NURBS equation of
motion represents the net effect of all applied forces. Typical force
functions are spring forces, repulsion forces, gravitational forces,
inflation forces, etc. [36, 6, 34].
For example, consider connecting a material point 
of a
D-NURBS surface to a point 
in space with an ideal Hookean
spring of stiffness k. The net applied spring force is
where is the 
is the unit delta function.
Equation (19) implies that 
and vanishes elsewhere on
the surface, but we can generalize it by replacing the
function with a smooth kernel (e.g., a unit Gaussian) to spread the
applied force over a greater portion of the surface. Furthermore, the
points and need not be constant, in general. We
can control either or both using a mouse to obtain an interactive
spring force.
