Physics-Based NURBS Swung Surfaces

We develop a dynamic, free-form surface model which is useful for representing a broad class of objects with symmetries and topological variability. The new model is based upon swung NURBS surfaces, and it inherits their desirable cross-sectional design properties. It melds these geometric features with the demonstrated conveniences of surface design within a physics-based framework. We demonstrate several applications of dynamic NURBS swung surfaces, including interactive sculpting through the imposition of forces and the adjustment of physical parameters such as mass, damping, and elasticity. Additional applications include surface design with geometric and physical constraints, by rounding solids, and through the fitting of unstructured data. We derive the equations of motion for the dynamic NURBS swung surface model using Lagrangian mechanics of an elastic surface and the finite element method. Finally we show that these surfaces are a special case of D-NURBS surfaces, a recently proposed physicsbased generalization of standard geometric NURBS.