Computer-Implemented Method of Computing, In A Computer Aided Design System, Of A Boundary Of A Modeled Object

{
  "publication_number": "US2010121626A1",
  "country": "US",
  "kind": "A1",
  "title": "Computer-Implemented Method of Computing, In A Computer Aided Design System, Of A Boundary Of A Modeled Object",
  "abstract": "The invention relates to a computer-implemented method of computing, in a computer aided design system, of a boundary of a modeled object, the method comprising: accessing data defining a modeled object as a simplicial m-complex; projecting the simplicial m-complex in n, m≧n; computing a polyhedral boundary of said modeled object as a polyhedral n−1-cycle in the projection of the simplicial complex, the polyhedral n−1-cycle substantially bordering the projection of the simplicial complex. The present invention is further directed to a computer program product and a computerized system comprising means for taking steps of the method of the invention.",
  "claims": [
    "1. A computer-implemented method of computing, in a computer aided design system, of a boundary of a modeled object, the method comprising: accessing data defining a modeled object as a simplicial m-complex; projecting the simplicial m-complex in n, m≧n; computing a polyhedral boundary of said modeled object as a polyhedral n−1-cycle in the projection of the simplicial complex, the polyhedral n−1-cycle substantially bordering the projection of the simplicial complex. 2. The method of claim 1, wherein at the step of computing, the polyhedral n−1-cycle comprises simplices of the projection of the simplicial complex. 3. The method of claim 2, wherein n=3 and the step of computing a polyhedral boundary comprises: testing triangles of the projection of the simplicial complex, wherein testing said triangles comprises, for each of the triangles tested, testing whether simplex cofaces of the triangle tested are on the same side of said each of the triangles tested. 4. The method of claim 1, wherein, at the step of accessing data, said simplicial complex is a simplicial product. 5. The method of claim 4, wherein, at the step of accessing data, said simplicial complex is a simplicial product of a polyhedral profile of a given object by a sequence of translations and/or transformations. 6. The method of claim 4, wherein, at the step of accessing data, said simplicial complex is a simplicial product of a polyhedral profile of a given object by a simplicial complex in a space of translations and/or transformations. 7. The method of claim 6, wherein said simplicial product is representative of a space swept by said polyhedral profile along said simplicial complex in the space of translations and/or transformations. 8. The method of claim 6, wherein said simplicial complex in a space of translations and/or transformations is a k-dimensional complex product of k sequences of translations and/or transformations. 9. The method of claim 7, wherein said simplicial complex in the space of translations and/or transformations is a 3D polyhedron in the space of translations and/or transformations. 10. The method of claim 5, wherein the simplicial product is representative of a space swept by said profile along said sequence. 11. The method of claim 4, further comprising, before the step of accessing data, a step of computing said simplicial product. 12. The method of claim 11, wherein the step of computing said simplicial product comprises: accessing data defining said polyhedral profile and said polyhedral trajectory; computing a Cartesian product from said polyhedral profile and said polyhedral trajectory; and carrying out a generalized triangulation of the computed Cartesian product. 13. A computer readable medium having computer program instructions stored thereon for computing a boundary of a modeled object, that when executed by a computer, they cause said computer to take the steps of: accessing data defining a modeled object as a simplicial m-complex; projecting the simplicial m-complex in n, m≧n; computing a polyhedral boundary of said modeled object as a polyhedral n−1-cycle in the projection of the simplicial complex, the polyhedral n−1-cycle substantially bordering the projection of the simplicial complex. 14. The computer readable medium of claim 13, wherein, at the step of computing, the polyhedral n−1-cycle comprises simplices of the projection of the simplicial complex. 15. The computer readable medium of claim 14, wherein n=3 and the step of computing a polyhedral boundary comprises: testing triangles of the projection of the simplicial complex, wherein testing said triangles comprises, for each of the triangles tested, testing whether simplex cofaces of the triangle tested are on the same side of said each of the triangles tested. 16. The computer readable medium of claim 15, further comprising: at the step of accessing data, said simplicial complex is a simplicial product; and before the step of accessing data, a step of computing said simplicial product, wherein the step of computing said simplicial product comprises: accessing data defining said polyhedral profile and said polyhedral trajectory; computing a Cartesian product from said polyhedral profile and said polyhedral trajectory; and carrying out a generalized triangulation of the computed Cartesian product. 17. Apparatus of computing, in a computer aided design system, of a boundary of a modeled object, the apparatus comprising: means for accessing data defining a modeled object as a simplicial m-complex; means for projecting the simplicial m-complex in n, m≧n; means for computing a polyhedral boundary of said modeled object as a polyhedral n−1-cycle in the projection of the simplicial complex, the polyhedral n−1-cycle substantially bordering the projection of the simplicial complex. 18. The apparatus of claim 17, wherein the polyhedral n−1-cycle comprises simplices of the projection of the simplicial complex. 19. The apparatus of claim 18, wherein n=3 and the means for computing a polyhedral boundary comprises: means for testing triangles of the projection of the simplicial complex, wherein testing said triangles comprises, for each of the triangles tested, testing whether simplex cofaces of the triangle tested are on the same side of said each of the triangles tested. 20. The apparatus of claim 19, wherein said simplicial complex is a simplicial product, and further comprising: means for computing said simplicial product, wherein said means for computing said simplicial product comprises: means for accessing data defining said polyhedral profile and said polyhedral trajectory; means for computing a Cartesian product from said polyhedral profile and said polyhedral trajectory; and means for carrying out a generalized triangulation of the computed Cartesian product."
  ],
  "description_excerpt": "The invention relates to the field of computers programs and systems, and more specifically to the field of computer-aided design (CAD), manufacturing (CAM), and engineering (CAE) systems.\n\nA number of systems and programs are offered on the market for the design of parts, assemblies of parts and products thereof, such as the one provided by Dassault Systémes under the trademark CATIA (Computer Aided Three Dimensional Interactive Application). CATIA is a multi-platform CAD/CAM/CAE software suite, commonly referred to as a 3D Product Lifecycle Management (PLM) software suite. It supports multiple stages of product development (CAx), ranging from conceptualization, through design (CAD) and manufacturing (CAM), until analysis (CAE). This software suite is customizable via application programming interfaces (API). Some versions can be adapted in various programming languages, under dedicated APIs.\n\nThese so-called CAD systems notably allow a user to construct and manipulate complex three dimensional (3D) models of objects or assemblies of objects. CAD systems thus provide a representation of modeled objects using edges or lines, in certain cases with faces. These CAD systems manage parts or assemblies of parts as modeled objects, which are mainly specifications of geometry. In particular, CAD files contain specifications, from which geometry is generated. From geometry, a representation is generated. Specifications, geometry and representation may be stored in a single CAD file or multiple ones.",
  "cpc": [
    "G06T 17/10",
    "G06F 30/00",
    "G06F 30/18"
  ],
  "ipc": [
    "G06F 17/50"
  ],
  "assignees": [
    "Dassault Systemes SE"
  ],
  "inventors": [
    "Nicolas Montana",
    "Frédéric Chazal",
    "André Lieutier"
  ],
  "filing_date": "2009-10-30",
  "publication_date": "2010-05-13",
  "priority_date": "2008-11-07",
  "application_number": "US-61001609-A",
  "family_id": "40456971",
  "cited_by_count": 26,
  "citations": [
    "US5566281A",
    "US5537519A",
    "US5850229A",
    "US7526131B2"
  ]
}