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Abstract : |
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 fit 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 finite element method to represent the model as a continuous surface. We implement two versions of the sheet using two different finite elements. The first is a triangular, quintic finite element whose nodal variables comprise the position of the surface plus its first and second partial derivatives. This element is "natural " in the sense that the nodal variables reflect each of the partial derivatives that occur in the spline's strain energy functional. The partial derivatives are useful in measuring the differential geometric properties of the fitted surface. The second element is a rectangular, bicubic finite 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 different sensing technologies related to CAGD and terrain mapping., |
