We consider a D-NURBS curve arc or surface patch defined by consecutive knots in the parametric domain to be a type of finite element. We define an element data structure which contains the geometric specification of the D-NURBS element along with its physical properties. A complete D-NURBS curve or surface is then implemented as a data structure which consists of an ordered array of D-NURBS curve or surface elements with additional information.
The element structure includes pointers to the associated generalized
coordinates (control points and weights). For instance, 9 control
points and associated weights are needed to describe a patch of a
quadratic D-NURBS surface (the total number of degrees of freedom is
36). The generalized coordinates associated with the entire D-NURBS
curve or surface are stored in the global vector 
. Note that
neighboring elements will share some generalized coordinates. The
shared variables will have multiple pointers impinging on them.
We also allocate in each D-NURBS element an elemental mass, damping,
and stiffness matrix, and include in the element data structure the
quantities needed to compute these matrices. These quantities include
the mass 
, damping 
, and elasticity
, 
density functions, which may
be represented as analytic functions or as parametric arrays of sample
values.