To date, however, they have been viewed as purely geometric primitives that require the user to manually adjust multiple control points and associated weights in order to design shapes. Their dynamic behavior results from the numerical integration of a set of nonlinear differential equations that automatically evolve the control points and weights in response to the applied forces and constraints. This energy depends on mass, damping, and elasticity density functions. The paper is well written, but the reader needs to know classical Lagrangian mechanics to understand the material. Because of the overwhelming number of model parameters that are available for the user, the density functions are chosen to be uniform or zero, the forces are limited to spring forces applied to single points, and the constraints are linear.
Nothing is said about the knot vector, which defines the parameterization.
This vector is of particular interest, since the authors have chosen a parameterization-dependent elasticity functional. The Digital Library is published by the Association for Computing Machinery.