Abstract: Methods, systems, and apparatus, including medium-encoded computer program products, for computer aided design of structures include, in one aspect, a method for producing, the method including: obtaining a polygonal control mesh for a smooth surface representing an object; subdividing the polygonal control mesh in one or more subdivisions to produce a refined control mesh, wherein the subdividing comprises: using data defining an eigen polyhedron around an extraordinary point in the polygonal control mesh to generate adjustment rules to determine positions of the extraordinary point, and face points and edge points for faces adjacent to the extraordinary point, and determining, according to the adjustment rules, the positions for the extraordinary point, the face points, and the edge points for the faces adjacent to the extraordinary point; and generating, by the computer graphics application, the smooth surface for output from the refined control mesh.

Abstract: Methods, systems, and apparatus, including medium-encoded computer program products, for computer aided design of structures include, in one aspect, a method for producing, the method including: obtaining a polygonal control mesh for a smooth surface representing an object; subdividing the polygonal control mesh in one or more subdivisions to produce a refined control mesh, wherein the subdividing comprises: using data defining an eigen polyhedron around an extraordinary point in the polygonal control mesh to generate adjustment rules to determine positions of the extraordinary point, and face points and edge points for faces adjacent to the extraordinary point, and determining, according to the adjustment rules, the positions for the extraordinary point, the face points, and the edge points for the faces adjacent to the extraordinary point; and generating, by the computer graphics application, the smooth surface for output from the refined control mesh.

Abstract: Methods, systems, and apparatus, including medium-encoded computer program products, for computer aided design of physical structures include, in one aspect, a method for increasing smoothness between a set of adjoining surface patches includes: identifying surface patches corresponding to a portion of a modeled surface to be smoothed, where the surface patches are defined by control vertices from a control mesh; smoothing the portion of the modeled surface based on continuity, where the smoothing includes determining a continuity measure at an interface between each pair of adjoining surface patches, and modifying positions of a subset of the control vertices, thereby modifying the surface patches, by targeting an overall improvement in the continuity measures for the interfaces, while also targeting an overall minimum of modification of positions of the control vertices; and processing the modified positions of the subset of the control vertices within the modelled surface for output.

Abstract: Methods, systems, and apparatus, including medium-encoded computer program products, for computer aided design of physical structures include, in one aspect, a method for increasing smoothness between a set of adjoining surface patches includes: identifying surface patches corresponding to a portion of a modeled surface to be smoothed, where the surface patches are defined by control vertices from a control mesh; smoothing the portion of the modeled surface based on continuity, where the smoothing includes determining a continuity measure at an interface between each pair of adjoining surface patches, and modifying positions of a subset of the control vertices, thereby modifying the surface patches, by targeting an overall improvement in the continuity measures for the interfaces, while also targeting an overall minimum of modification of positions of the control vertices; and processing the modified positions of the subset of the control vertices within the modelled surface for output.