Abstract: It is provided a computer-implemented method for designing a three-dimensional modeled object. The method comprises providing geometrical elements that represent the modeled object and that include a set in which the geometrical elements are a copy one of another. The method also comprises defining a graph, determining maximal sub-graphs of the graph, and identifying, within the determined sub-graphs, the set of connected components having the highest number of arcs and for which the rigid motions represented by the arcs all respect the identity criterion. Such a method improves the design of a 3D modeled object.

Abstract: Provided is a computer-implemented method for updating a 3D model. The method comprises providing an operation undergone by the 3D model, an old input graph of the 3D model before undergoing the operation, an old output graph of the 3D model corresponding to an application of the operation to the old input graph, and a new input graph of the operation. The new input graph is generated as a result of a modification of the 3D model. The method also comprises computing a double push-out rewriting rule that specifies a part of the old input graph to be replaced, a part of the new input graph to replace the part of the old input graph. The rewriting rule also specifies an interface which is a part common to the part of the old input graph, the part of the new input graph, and the old output graph. The method further comprises applying the rewriting rule directly on the old output graph. This transforms the old output graph to a new output graph representing an updated 3D model of the real world object.

Abstract: It is provided a computer-implemented method for designing a three-dimensional modeled object. The method comprises providing geometrical elements that represent the modeled object and that include a set in which the geometrical elements are a copy one of another. The method also comprises defining a graph, determining maximal sub-graphs of the graph, and identifying, within the determined sub-graphs, the set of connected components having the highest number of arcs and for which the rigid motions represented by the arcs all respect the identity criterion. Such a method improves the design of a 3D modeled object.

Abstract: It is provided a computer-implemented method for updating a modeled object. The method comprises providing an operation, an old input graph of the operation, an old output graph corresponding to an application of the operation to the old input graph, a new input graph of the operation. The method also comprises computing a rewriting rule that specifies a replaced which is a part of the old input graph to be replaced, a replacement which is a part of the new input graph to replace the replaced, an interface which is a part common to the replaced, the replacement and the old output graph. The method further comprises applying the rewriting rule to the old output graph. The method is an improvement to updating a modeled object.