Dynamic NURBS Swung Surfaces for Physics - BasedShape

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 tting 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 nite element method. We also show that these surfaces are a special case of D-NURBS surfaces, a recently proposed physics-based generalization of standard geometric NURBS. Our free-form, rational model not only provides a systematic and uniied approach for a variety of CAGD problems such as constraint-based optimization, variational design, automatic weight selection, shape approximation, etc., but it also supports interactive sculpting using physics-based manipulation tools. (a) (b) Figure 1: Construction of a cubical NURBS swung surface. (a) NURBS proole curve on x-z plane, NURBS trajectory curve on x-y plane. (b) Cube surface wireframe.