A system for element quality improvement in three-dimensional quadrilateral-dominant surface meshes comprising: at least one processor configured to: determine a first plurality of edges (608, 810) of a plurality of quadrilateral elements (604, 606, 806) that form a surface mesh of a 3D model, which edges have lengths that are shorter than a first predetermined minimum element edge length; collapse in the mesh the determined first plurality of edges to convert each quadrilateral element that included a respective one of the collapsed first plurality of edges into a respective triangular element (702, 704, 812, 814); after the first plurality of edges are collapsed, determine a second plurality of edges (904, 1004, 1204) of the plurality of quadrilateral elements (902, 1010, 1202) that are shorter than a second predetermined minimum element edge length and that are longer than the first predetermined minimum element edge length; move in the mesh a plurality of nodes (908, 1002, 1208, 1210) connected to at least some of the second plurality of edges so that at least some of the second plurality of edges have lengths that are at least the second predetermined minimum element edge length; determine all remaining edges of the plurality of quadrilateral elements that are shorter than the second predetermined minimum element edge length; and collapse in the mesh the determined remaining edges to convert each quadrilateral element that included a respective collapsed one of the remaining edges into a respective triangular element, whereby a modified surface mesh is produced in which all quadrilaterals in the modified mesh have edge lengths that are at least the second predetermined minimum element edge length. determine a first plurality of edges (608, 810) of a plurality of quadrilateral elements (604, 606, 806) that form a surface mesh of a 3D model, which edges have lengths that are shorter than a first predetermined minimum element edge length; collapse in the mesh the determined first plurality of edges to convert each quadrilateral element that included a respective one of the collapsed first plurality of edges into a respective triangular element (702, 704, 812, 814); after the first plurality of edges are collapsed, determine a second plurality of edges (904, 1004, 1204) of the plurality of quadrilateral elements (902, 1010, 1202) that are shorter than a second predetermined minimum element edge length and that are longer than the first predetermined minimum element edge length; move in the mesh a plurality of nodes (908, 1002, 1208, 1210) connected to at least some of the second plurality of edges so that at least some of the second plurality of edges have lengths that are at least the second predetermined minimum element edge length; determine all remaining edges of the plurality of quadrilateral elements that are shorter than the second predetermined minimum element edge length; and collapse in the mesh the determined remaining edges to convert each quadrilateral element that included a respective collapsed one of the remaining edges into a respective triangular element, whereby a modified surface mesh is produced in which all quadrilaterals in the modified mesh have edge lengths that are at least the second predetermined minimum element edge length.