We discretize the motion equations using the following finite
differences in 
( 
in the case of geometric
constraints):
We obtain the discrete form of (17) as
In this and the following explicit time integration schemes, all the
matrices are evaluated at time t (instead of time 
as in
the implicit schemes).
For D-NURBS surfaces with linear geometric constraints, (22) is discretized as
For the D-NURBS curve, we substitute 
with 
in
(47) and (48).
The discretized forms of the simplified first order equations of motion (32) and (33) are
and
