We have developed dynamic NURBS, a physics-based generalization of the well-known geometric NURBS curves and surfaces. D-NURBS were derived systematically through the application of Lagrangian mechanics and implemented using concepts from finite element analysis and efficient numerical methods. We generalized our D-NURBS formulation to incorporate geometric constraints. The formulation extends naturally to solids, albeit at proportionately greater computational cost.
We described a prototype interactive modeling system based on D-NURBS and demonstrated the flexibility of our models in a variety of applications. When working with D-NURBS, a designer need not manipulate the individual degrees of freedom of an object. Instead, the designer can work with sculpting tools that are implemented in terms of forces and geometric constraints. Sculpting forces may be applied interactively to move the object or refine its shape. The interactive response of the D-NURBS may be modified by varying its mass and damping distributions. Global design requirements may also be achieved by varying physical parameters such as elastic energies.
Because NURBS have been assimilated into such industry standards such as IGES, PHIGS+, and OpenGL, our dynamic NURBS model promises to forge stronger links between established CAGD methodologies and new techniques in physics-based modeling.