# US 10,311,182 B2 · Topological change in a constrained asymmetrical subdivision mesh > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 10,311,182 B2 - Document ID: US10311182B2 - Status: Granted - Kind: B2 - Application number: 15/238,227 - Filed: 2016-08-16 - Published: 2017-06-22 - Granted: 2019-06-04 - Earliest claimed: 2015-12-16 - Assignees: Dassault Systemes - Applicants: Dassault Systemes - Inventors: Frederic Letzelter; Jean-Marc Chauvet; Christophe Dufau - Web page: https://patentgrep.com/patent/US10311182B2 ## CPC - G06F 30/23: using finite element methods [FEM] or finite difference methods [FDM] - G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N) ## Abstract Embodiments provide methods and systems for modifying a finite element mesh representation of a three-dimensional model. A method according to an embodiment defines a symmetric constraint of a finite element mesh where the finite element mesh represents a subject 3D model and the symmetric constraint comprises two asymmetric zones of the finite element mesh to be modified symmetrically. Next, corresponding finite elements between the two asymmetric zones are identified and a topological manipulation to at least one of the identified corresponding finite elements is performed. In response, the topological manipulation is performed symmetrically on the identified finite element corresponding to the at least one finite element. In such an embodiment, performing the manipulation symmetrically results in the two asymmetric zones being modified symmetrically and represents a symmetrical topological modification in the subject 3D model. ## Claims ### Claim 1 A computer-implemented method of modifying a finite element mesh representing a computer aided design (CAD) 3D model representing a real-world object, the method comprising: by a user, defining a symmetric constraint of a finite element mesh using a graphical user interface coupled to a processor, the finite element mesh representing a subject CAD 3D model including a shape of the subject CAD 3D model, the symmetric constraint comprising two asymmetric zones of the finite element mesh to be modified symmetrically; automatically identifying, by the processor, existing corresponding finite elements between the two asymmetric zones; performing by the user, user-interactively through the graphical user interface, a topological manipulation to at least one finite element of the two asymmetric zones; and performing automatically by the processor a symmetrical topological manipulation on the identified existing finite element corresponding to the at least one finite element, such that the symmetrical manipulation results in the two asymmetric zones of the finite element mesh being topologically modified symmetrically, thereby representing a symmetrical topological modification to the shape of the subject CAD 3D model. ### Claim 2 (depends on 1) The method of claim 1 wherein identifying corresponding finite elements between the two asymmetric zones comprises: identifying symmetric edges, vertices, and faces of the two asymmetric zones. ### Claim 3 (depends on 1) The method of claim 1 further comprising: determining a local symmetric plane defined by a barycenter of the two asymmetric zones of the finite element mesh and normal to a direction defined by the two asymmetric zones of the finite element mesh; and updating the symmetric constraint and the identified corresponding finite elements to reflect the performed topological manipulations using the determined local symmetric plane. ### Claim 4 (depends on 3) The method of claim 3 wherein updating the symmetric constraint comprises: reconstructing a respective edge contour associated with each of the two asymmetric zones; and reconstructing a respective border face associated with each of the two asymmetric zones. ### Claim 5 (depends on 1) The method of claim 1 wherein the topological manipulation comprises at least one of: a face extrusion; an edge cut; a face subdivision; a bevel; and a face removal. ### Claim 6 (depends on 1) The method of claim 1 wherein the symmetric constraint applies only to a subpart of the finite element mesh. ### Claim 7 (depends on 1) The method of claim 1 wherein defining a symmetric constraint comprises at least one of: identifying a first group of connected faces and a second group of connected faces; identifying a plane and a group of connected faces; identifying a group of faces; and identifying a plane. ### Claim 8 (depends on 1) The method of claim 1 wherein elements of the two asymmetric zones of the finite element mesh are identified with respective unique tags. ### Claim 9 (depends on 1) The method of claim 1 wherein defining the symmetric constraint comprises: determining a separating shape between the two asymmetric zones. ### Claim 10 (depends on 9) The method of claim 9 wherein the separating shape is a plane. ### Claim 11 (depends on 9) The method of claim 9 wherein the separating shape is used in identifying the corresponding finite elements between the two asymmetric zones. ### Claim 12 A computer system for modifying a finite element mesh representing a computer aided design (CAD) 3D model representing a real-world object, the computer system comprising: a processor; and a memory with computer code instructions stored thereon, the processor and the memory, with the computer code instructions being configured to cause the system to: implement, by a user, defining a symmetric constraint of a finite element mesh using a graphical user interface coupled to the processor, the finite element mesh representing a subject CAD 3D model including a shape of the subject CAD 3D model, the symmetric constraint comprising two asymmetric zones of the finite element mesh to be modified symmetrically; automatically identify, by the processor, existing corresponding finite elements between the two asymmetric zones; implement the user performing, user-interactively through the graphical user interface, a topological manipulation to at least one finite element of the two asymmetric zones; and perform automatically by the processor a symmetrical topological manipulation on the identified existing finite element corresponding to the at least one finite element, such that the symmetrical manipulation results in the two asymmetric zones of the finite element mesh being topologically modified symmetrically, thereby representing a symmetrical topological modification to the shape of the subject CAD 3D model. ### Claim 13 (depends on 12) The system of claim 12 wherein, in identifying corresponding finite elements between the two asymmetric zones, the processor and the memory, with the computer code instructions, are further configured to cause the system to: identify symmetric edges, vertices, and faces of the two asymmetric zones. ### Claim 14 (depends on 12) The system of claim 12 wherein the processor and the memory, with the computer code instructions, are further configured to cause the system to: determine a local symmetric plane defined by a barycenter of the two asymmetric zones of the finite element mesh and normal to a direction defined by the two asymmetric zones of the finite element mesh; and update the symmetric constraint and the identified corresponding finite elements to reflect the performed topological manipulations using the determined local symmetric plane. ### Claim 15 (depends on 14) The system of claim 14 wherein, in updating the symmetric constraint, the processor and the memory, with the computer code instructions, are further configured to cause the system to: reconstruct a respective edge contour associated with each of the two asymmetric zones; and reconstruct a respective border face associated with each of the two asymmetric zones. ### Claim 16 (depends on 12) The system of claim 12 wherein the topological manipulation comprises at least one of: a face extrusion; an edge cut; a face subdivision; a bevel; and a face removal. ### Claim 17 (depends on 12) The system of claim 12 wherein the symmetric constraint applies only to a subpart of the finite element mesh. ### Claim 18 (depends on 12) The system of claim 12 wherein defining a symmetric constraint comprises at least one of: identifying a first group of connected faces and a second group of connected faces; identifying a plane and a group of connected faces; identifying a group of faces; and identifying a plane. ### Claim 19 (depends on 12) The system of claim 12 wherein elements of the two asymmetric zones of the finite element mesh are identified with respective unique tags. ### Claim 20 (depends on 12) The system of claim 12 wherein defining the symmetric constraint comprises: determining a separating shape between the two asymmetric zones. ### Claim 21 (depends on 20) The system of claim 20 wherein the separating shape is a plane. ### Claim 22 (depends on 20) The system of claim 20 wherein the separating shape is used in identifying the corresponding finite elements between the two asymmetric zones. ### Claim 23 A computer program product for modifying a finite element mesh representing a computer aided design (CAD) 3D model representing a real-world object, the computer program product comprising computer-readable instructions stored on a non-transitory computer readable medium responsive to execution by a computing device that causes the computing device to perform operations comprising: implementing by a user, defining a symmetric constraint of a finite element mesh using a graphical user interface coupled to a processor, the finite element mesh representing a subject CAD 3D model including a shape of the subject CAD 3D model, the symmetric constraint comprising two asymmetric zones of the finite element mesh to be modified symmetrically; automatically identifying, by the processor, existing corresponding finite elements between the two asymmetric zones; implementing the user performing, user-interactively through the graphical user interface, a topological manipulation to at least one finite element of the two asymmetric zones; and performing automatically by the processor a symmetrical topological manipulation on the identified existing finite element corresponding to the at least one finite element, such that the symmetrical manipulation results in the two asymmetric zones of the finite element mesh being topologically modified symmetrically, thereby representing a symmetrical topological modification to the shape of the subject CAD 3D model.