The kinetic energy associated with element

This paper presents a physics-based approach to surface reconstruction using an elastically deformable \sheet" model. The model is based on a thin-plate under tension spline which deforms to t visual data according to internal forces stemming from the elastic properties of the surface and external forces which are produced from the data. We employ the nite element method to represent the model as a continuous surface. We implement two versions of the sheet using two diierent nite elements. The rst is a triangular, quintic nite element whose nodal variables comprise the position of the surface plus its rst and second partial derivatives. This element is \natural" in the sense that the nodal variables reeect each of the partial derivatives that occur in the spline's strain energy functional. The partial derivatives are useful in measuring the diierential geometric properties of the tted surface. The second element is a rectangular, bicubic nite element whose nodal variables also include some of the partial derivatives of the surface. We apply the sheet model to the reconstruction of various 3D data sets generated by several diierent sensing technologies related to CAGD and terrain mapping.