Dynamic swung surfaces for physics-based shape design

Hong Qin, Demetri Terzopoulos

Abstract: A dynamic, freeform surface model which is useful for representing a broad class of objects with symmetries and topological variability is developed. The new model is based upon swung NURBS surfaces, and it inherits their desirable crosssectional design properties. It melds these geometric features with the demonstrated convenience of surface design within a physics-based framework. Several applications of dynamic NURBS swung surfaces are demonstrated, 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. The equations of motion for the dynamic NURBS swung surface model are derived using the Lagrangian mechanics of an elastic surface and the finite element method. It is also shown that these surfaces are a special case of d-NURBS surfaces, a recently proposed physics-based generalization of standard geometric NURBS. The freeform, rational model not only provides a systematic and unified approach for a variety of cagd problems such as constraint-based optimization, variational design, automatic weight selection, and shape approximation, but it also supports interactive sculpting using physics-based manipulation tools.