A system and program product for re-meshing of a three-dimensional (3D) input model using progressive implicit approximating levels are provided. Specifically, an initial quadrilateral mesh for a 3D input model is provided. Then, an implicit approximating field is built for a first approximating level (L) of the 3D input model using an implicit surface modeling technique. An iso-contour of the implicit approximating field is then extracted, and the quadrilateral mesh is fit to the first approximating level (L). The fit between the quadrilateral mesh and the first approximating level (L) is then estimated, and it is determined whether the fit meets a predetermined quality criterion. If not, the quadrilateral mesh is refined using one or more of a sequence of topological operations are performed to improve the fit. The process is then iteratively repeated for subsequent approximation levels until one of the subsequent approximation levels is fit to the 3D input model.
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