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 computer-implemented method for civil engineering including obtaining a mesh representing a terrain and a polyline on the mesh, the method further includes computing a contributor of the polyline. The computing of the contributor includes modifying the mesh by determining, based on the polyline, a trench below the polyline. The computing of the contributor further includes computing a watershed segmentation of the terrain based on the modified mesh. The computing of the contributor further includes, based on the computed watershed segmentation, identifying, on the modified mesh, a basin comprising the trench. The contributor corresponds to the identified basin.

Abstract: A computer-implemented method for learning an autoencoder notably is provided. The method includes obtaining a dataset of images. Each image includes a respective object representation. The method also includes learning the autoencoder based on the dataset. The learning includes minimization of a reconstruction loss. The reconstruction loss includes a term that penalizes a distance for each respective image. The penalized distance is between the result of applying the autoencoder to the respective image and the set of results of applying at least part of a group of transformations to the object representation of the respective image. Such a method provides an improved solution to learn an autoencoder.

Abstract: Computer-implemented method for civil engineering including obtaining a mesh representing a terrain and computing a watershed segmentation of the terrain based on the mesh, the computing of the watershed segmentation including identifying one or more saddle points on the mesh, for each identified saddle point, identifying paths each ascending from the saddle point according to a direction of a local maximal slope around the saddle point, and a path descending from the saddle point according to a direction of a steepest slope around the saddle point, the identified ascending paths dividing the mesh into connected components, and, for each identified saddle point, merging each connected component of which bottom point is the saddle point with a connected component including the identified path descending from the saddle point according to a direction of a steepest slope. The merging yields at least a part of a basin.

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 computer-implemented method for 3D reconstruction of a structure of a real scene including obtaining a 3D point cloud representing the structure. The method further includes determining a closed triangulated surface representing a skin of the structure. The determining explores candidate closed triangulated surfaces each meshing at least a respective part of the 3D point cloud. The determining penalizes a high rank of the candidate closed triangulated surfaces according to a lexicographic order. The lexicographic order is based on a triangle order and orders a first candidate closed triangulated surface having first triangles which are ordered according to a decreasing rank of the triangle order, relative to a second candidate closed triangulated surface having second triangles which are ordered according to a decreasing rank of the triangle order. The triangle order penalizes a triangle size. This constitutes an improved method for 3D reconstruction of a structure of a real scene.

Abstract: A computer-implemented method for civil engineering is described that includes obtaining a watershed segmentation of a terrain. The watershed segmentation includes basins. The method further includes merging first basins of the watershed segmentation that each verify a smallness criterion, each with a second basin downstream to the first basin.

Abstract: Computer-implemented method for civil engineering including obtaining a mesh representing a terrain and computing a watershed segmentation of the terrain based on the mesh, the computing of the watershed segmentation including identifying one or more saddle points on the mesh, for each identified saddle point, identifying paths each ascending from the saddle point according to a direction of a local maximal slope around the saddle point, and a path descending from the saddle point according to a direction of a steepest slope around the saddle point, the identified ascending paths dividing the mesh into connected components, and, for each identified saddle point, merging each connected component of which bottom point is the saddle point with a connected component including the identified path descending from the saddle point according to a direction of a steepest slope. The merging yields at least a part of a basin.

Abstract: A computer-implemented method for civil engineering including obtaining a mesh representing a terrain and a polyline on the mesh, the method further includes computing a contributor of the polyline. The computing of the contributor includes modifying the mesh by determining, based on the polyline, a trench below the polyline. The computing of the contributor further includes computing a watershed segmentation of the terrain based on the modified mesh. The computing of the contributor further includes, based on the computed watershed segmentation, identifying, on the modified mesh, a basin comprising the trench. The contributor corresponds to the identified basin.

Abstract: A computer-implemented method for learning an autoencoder notably is provided. The method comprises providing a dataset of images. Each image includes a respective object representation. The method also comprises learning the autoencoder based on the dataset. The learning includes minimization of a reconstruction loss. The reconstruction loss includes a term that penalizes a distance for each respective image. The penalized distance is between the result of applying the autoencoder to the respective image and the set of results of applying at least part of a group of transformations to the object representation of the respective image. Such a method provides an improved solution to learn an autoencoder.

Abstract: A computer-implemented method for 3D reconstruction of a structure of a real scene including obtaining a 3D point cloud representing the structure. The method further includes determining a closed triangulated surface representing a skin of the structure. The determining explores candidate closed triangulated surfaces each meshing at least a respective part of the 3D point cloud. The determining penalizes a high rank of the candidate closed triangulated surfaces according to a lexicographic order. The lexicographic order is based on a triangle order and orders a first candidate closed triangulated surface having first triangles which are ordered according to a decreasing rank of the triangle order, relative to a second candidate closed triangulated surface having second triangles which are ordered according to a decreasing rank of the triangle order. The triangle order penalizes a triangle size. This constitutes an improved method for 3D reconstruction of a structure of a real scene.

Abstract: A computer-implemented method for learning an autoencoder notably is provided. The method includes obtaining a dataset of images. Each image includes a respective object representation. The method also includes learning the autoencoder based on the dataset. The learning includes minimization of a reconstruction loss. The reconstruction loss includes a term that penalizes a distance for each respective image. The penalized distance is between the result of applying the autoencoder to the respective image and the set of results of applying at least part of a group of transformations to the object representation of the respective image. Such a method provides an improved solution to learn an autoencoder.

Abstract: A computer-implemented method queries a database that comprises modeled objects. Each modeled object represents a physical attribute of a respective real object. The database comprises for each modeled object, a respective simplicial complex. The method comprises providing a query that includes a signature criterion, and returning, as results of the query, respective modeled objects of the database. The respective modeled object is returned based on an extent to which the respective modeled object has a respective simplicial complex that respects the signature criterion. Such method system improves the field of searching modeled objects in a database.

Abstract: It is provided a computer-implemented method for designing a modeled volume. The method comprises providing a set of dexels that represents the modeled volume, each dexel comprising a set of at least one segment representing the intersection between a line and the modeled volume, wherein the set of dexels is partitioned into groups of neighboring dexels, and wherein a memory space depending on the maximum number of segments comprised in each of the dexels of the group is allocated to each group; providing a sculpting operation on the modeled volume; and updating the set of dexels in response to the sculpting operation. Such a method improves the design of a modeled volume represented by a set of dexels.

Abstract: A computer-implemented method for learning an autoencoder notably is provided. The method comprises providing a dataset of images. Each image includes a respective object representation. The method also comprises learning the autoencoder based on the dataset. The learning includes minimization of a reconstruction loss. The reconstruction loss includes a term that penalizes a distance for each respective image. The penalized distance is between the result of applying the autoencoder to the respective image and the set of results of applying at least part of a group of transformations to the object representation of the respective image. Such a method provides an improved solution to learn an autoencoder.

Abstract: A computer-implemented method queries a database that comprises modeled objects. Each modeled object represents a physical attribute of a respective real object. The database comprises for each modeled object, a respective simplicial complex. The method comprises providing a query that includes a signature criterion, and returning, as results of the query, respective modeled objects of the database. The respective modeled object is returned based on an extent to which the respective modeled object has a respective simplicial complex that respects the signature criterion. Such method system improves the field of searching modeled objects in a database.

Abstract: It is provided a computer-implemented method for simulating the machining of a workpiece with a cutting tool having a cutting part and a non-cutting part. The method comprises providing a modeled volume representing the workpiece and a trajectory of the cutting tool; determining a colliding sweep of the cutting tool, wherein the colliding sweep represents the volume swept by the non-cutting front of the cutting tool when the cutting tool follows the trajectory; testing a collision with the workpiece according to the determining step. Such a method improves the simulation of the machining of a workpiece with a cutting tool.

Abstract: It is provided a computer-implemented method for designing a modeled volume. The method comprises providing a sculpting process on the modeled volume, initial lines, and an initial set of dexels that represents the modeled volume after going through the sculpting process and that is based on the initial lines; then providing new lines by refining the initial lines; and determining a new set of dexels that represents the modeled volume after going through the sculpting process and that is based on the new lines, wherein determining the new set of dexels comprises determining sets of at least one segment representing the intersection between each new line and the modeled volume before going through the sculpting process and then applying the sculpting process on the determined sets of at least one segment. The method improves designing a modeled volume represented by a set of dexels.

Abstract: The invention is directed to a computer-implemented process, in a computer-aided geometric design system, for computing a resulting closed triangulated polyhedral surface from a first and a second modeled objects. The first modeled object is modeled by a first closed triangulated polyhedral surface and the second modeled object is modeled by a second closed triangulated polyhedral surface.

Abstract: It is provided a computer-implemented method for simulating the machining of a workpiece with a cutting tool having a cutting part and a non-cutting part. The method comprises providing a modeled volume representing the workpiece and a trajectory of the cutting tool; determining a colliding sweep of the cutting tool, wherein the colliding sweep represents the volume swept by the non-cutting front of the cutting tool when the cutting tool follows the trajectory; testing a collision with the workpiece according to the determining step. Such a method improves the simulation of the machining of a workpiece with a cutting tool.