Finite element modeling method and computer system for converting a triangular mesh surface to a quadrilateral mesh surface

Claim 1

A method for converting triangular meshes to quadrilateral meshes in a computer system, the computer system comprising a processor, a means for inputting graphical data, the graphical data comprising at least one surface, the surface being defined by at least one boundary, the surface comprising at least one triangular mesh, the triangular mesh comprising at least one triangle, said triangle having edges and vertices, the method comprising the processor-executed steps of: (a) for at least one triangle, ascertaining the topological distance from the triangle to the boundary; (b) dividing the surface into at least one layer, the layer comprising at least one triangle, such that each layer comprises triangles having a topological distance within a predetermined range from the boundary; (c) for at least one layer, forming at least one group, the group comprising at least one triangle; and (d) dividing each group into at least three quadrilateral elements.

Claim 2

A method for converting triangular meshes to quadrilateral meshes in a computer system, the computer system comprising a processor, a means for inputting graphical data, the graphical data comprising at least one surface, the surface being defined by at least one boundary, the surface comprising at least one triangular mesh, the triangular mesh comprising at least one triangle, said triangle having edges and vertices, the method comprising the processor-executed steps of: (a) for at least one triangle, ascertaining the topological distance from the triangle to the boundary; (b) dividing the surface into at least one layer, the layer comprising at least one triangle, such that each layer comprises triangles having a topological distance within a predetermined range from the boundary; (c) for at least one layer, forming at least one group, the group comprising at least one triangle; and (d) dividing each group into at least three quadrilateral elements.

Claim 10

A method for converting triangular meshes to quadrilateral meshes in a computer system, the computer system comprising a processor, a means for inputting graphical data comprising at least one surface and at least one boundary, the surface comprising at least one triangular mesh, the triangular mesh comprising at least one triangle, the triangle having vertices and edges, the method comprising the processor-executed steps of: (a) preparing an adjoining graph for connecting adjacent triangles of the triangular mesh, the adjoining graph comprising points and adjoining edges, such that each triangle has one point, the point being inside the triangle, and adjoining edges connect points of adjacent triangles; (b) ascertaining the topological distance between at least one triangle and the boundary; (c) dividing the surface into at least one layer, the layer comprising at least one triangle, such that each layer comprises triangles having a topological distance within a predetermined range from the boundary; (d) traversing the points of the adjoining graph and removing the adjoining edge if the adjoining edge connects triangles in different layers; (e) traversing the points of the adjoining graph and removing the adjoining edge when combining the two triangles corresponding to the adjoining edge forms a concave quadrilateral; and (g) traversing the points of the adjoining graph and matching adjacent triangles to form triangle pairs; (h) forming quadrilaterals from matched triangle pairs and dividing the quadrilaterals into four quadrilateral elements; and (i) for triangles having no matched triangle, dividing the triangle into three quadrilateral elements.

Claim 11

A method for converting triangular meshes to quadrilateral meshes in a computer system, the computer system comprising a processor, a means for inputting graphical data comprising at least one surface and at least one boundary, the surface comprising at least one triangular mesh, the triangular mesh comprising at least one triangle, the triangle having vertices and edges, the method comprising the processor-executed steps of: (a) preparing an adjoining graph for connecting adjacent triangles of the triangular mesh, the adjoining graph comprising points and adjoining edges, such that each triangle has one point, the point being inside the triangle, and adjoining edges connect points of adjacent triangles; (b) ascertaining the topological distance between at least one triangle and the boundary; (c) dividing the surface into at least one layer, the layer comprising at least one triangle, such that each layer comprises triangles having a topological distance within a predetermined range from the boundary; (d) traversing the points of the adjoining graph and removing the adjoining edge if the adjoining edge connects triangles in different layers; (e) traversing the points of the adjoining graph and removing the adjoining edge when combining the two triangles corresponding to the adjoining edge forms a concave quadrilateral; and (g) traversing the points of the adjoining graph and matching adjacent triangles to form triangle pairs; (h) forming quadrilaterals from matched triangle pairs and dividing the quadrilaterals into four quadrilateral elements; and (i) for triangles having no matched triangle, dividing the triangle into three quadrilateral elements.