Abstract: A 3D reconstruction method including obtaining a first open triangulated surface consisting of triangles of a tetrahedral meshing of a point cloud and determining a second open triangulated surface. The determining explores candidate open triangulated surfaces each being a set of triangles of the meshing and penalizes a high rank of the candidates according to a lexicographic order based on a triangle order and ordering a candidate having triangles decreasingly ordered according to a triangle order penalizing triangle size, relative to another candidate having triangles decreasingly ordered according to the triangle order. The second surface violates consistency of a labelling of the meshing with two labels. A triangle respects labelling consistency when it belongs to the first surface and separates two tetrahedrons having different labels, or when it does not belong to the first surface and separates two tetrahedrons having a same label.

Abstract: A 3D reconstruction method including obtaining a first open triangulated surface consisting of triangles of a tetrahedral meshing of a point cloud and determining a second open triangulated surface. The determining explores candidate open triangulated surfaces each being a set of triangles of the meshing and penalizes a high rank of the candidates according to a lexicographic order based on a triangle order and ordering a candidate having triangles decreasingly ordered according to a triangle order penalizing triangle size, relative to another candidate having triangles decreasingly ordered according to the triangle order. The second surface violates consistency of a labelling of the meshing with two labels. A triangle respects labelling consistency when it belongs to the first surface and separates two tetrahedrons having different labels, or when it does not belong to the first surface and separates two tetrahedrons having a same label.

Abstract: The present invention relates to a computer-implemented method of computing. In one embodiment, computing a boundary of a modelled object in a computer aided design system, the method may include accessing data defining a modeled object as a simplicial m-complex. The method may further include projecting the simplicial m -complex in n, m?n. The method also may include computing a polyhedral boundary of the modeled object as a polyhedral n?1-cycle in the projection of the simplicial complex. The polyhedral n?1-cycle may substantially border the projection of the simplicial complex. The present invention is further directed to a computer program product and a computerized system for performing the method of the invention.

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.

Abstract: For modifying a zone of a surface having an original shape, outer constraints are defined at boundaries of the zone as continuities Gk along at least part thereof. Inner constraints Gn are defined as points or curves to be crossed by the zone when modified. An amount of deformation is defined in each point of the zone as a result of a resilient deformation of a generalized infinite thin planar plate in equilibrium, respecting the outer and inner constraints. The modified zone is generated as a surface resulting from a result of an application of the resilient deformation to the original shape in the zone and connected to the unmodified portion of the surface.