Deforming virtual objects interactively in accordance with an elastic model

We show how interactive deformations of a virtual 3D object can be carried out by using a hierarchical implementation of the finite element method (FEM). Basing deformations on the concepts of elasticity gives the human a measure of predictability when deciding where to apply forces to the object so that a desired shape would ensue. As is well known, one of the most powerful tools for analysing elasticity is the FEM, but the computational burden associated with a straightforward application of FEM to the problem at hand would make it too slow for any interactive process on even the fastest workstations. We have therefore developed a method in which the computational burden of FEM is alleviated by carrying out the FEM analysis at two different resolutions; a coarse resolution for a 3D calculation of the deformations and, subsequently, a finer resolution for just the surface layers of the object for a better (and smoother) delineation of the object shape. For the case of analysing the surface layers using the finer resolution, we show how a plate-theory version of FEM can be employed.