Method, system, and program product for re-meshing of a three-dimensional input model using progressive implicit approximating levels

A method for quadrilateral re-meshing of a three-dimensional (3D) input model using progressive implicit approximating levels, comprising:

• providing a quadrilateral mesh for the 3D input model;
• building an implicit approximating field for a first approximating level (L) of the 3D input model using an implicit surface modeling technique;
• extracting an iso-contour of the implicit approximating field;
• fitting the quadrilateral mesh to the first approximating level (L);
• estimating a fit between the quadrilateral mesh and the first approximating level (L);
• determining whether the fit meets a predetermined quality criterion;
• iteratively repeating the building, extracting, fitting, estimating, and determining for subsequent approximation levels until a predetermined stopping criterion is reached;
• and
• refining the initial quadrilateral mesh using at least one of a sequence of topological operations to achieve an improved fit after the determining step if the fit fails to meet the predetermined quality criterion;
• wherein the quadrilateral mesh is an initial quadrilateral mesh,
• and wherein the sequence of topological operations comprises snapping vertices, splitting edges, extruding faces, and bridging faces of the quadrilateral mesh.