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: 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 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: Disclosed is a computer-implemented method for determining a boundary representation of the result of a two-axis 3D printing process. The method comprises obtaining a stack of planes, each couple of consecutive planes corresponding to a respective slice of the result of the 3D printing process. The method also comprises, for each couple of consecutive planes: obtaining one or more respective tool trajectories, determining a respective 2D contour corresponding to the one or more tool trajectories. The method also comprises determining a respective extrusion of the respective 2D contour bounded by a second plane of the couple and a first plane of the couple, and forming the boundary representation with the extrusions and portions of the planes. The method improves 3D printing.

Abstract: It is provided a computer-implemented method for designing a 3D modeled object, comprising providing, to a computer system, a NURBS surface that represents the 3D modeled object and that is defined by a grid of control points; determining (S20), by the computer system, a grid of surface points that belong to the NURBS surface, the grid of surface points corresponding to the grid of control points according to a predetermined invertible function; displaying, by the computer system, the NURBS surface and, on the NURBS surface, the grid of surface points; selecting, by graphical user-interaction, a subset of the surface points; modifying, by graphical user-interaction, position of the selected subset of surface points, and accordingly, updating real-time, by the computer system, the surface, the update being performed according to the predetermined invertible function. Such a method improves the design of a 3D modeled object.

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: It is provided a computer-implemented method for simulating the machining of a workpiece with a cutting tool having at least one cutting part and at least one non-cutting part. The method comprises providing a set of dexels that represents the workpiece, a trajectory of the cutting tool, and a set of meshes each representing a respective cutting part or non-cutting part of the cutting tool. And then the method comprises for each dexel computing, for each mesh, the extremity points of all polylines that describe a time diagram, and testing a collision of the cutting tool with the workpiece along the dexel based on the lower envelope of the set of all polylines. Such a method improves the simulating of the machining of a workpiece.

Abstract: Disclosed is a computer-implemented method for determining a boundary representation of the result of a two-axis 3D printing process. The method comprises obtaining a stack of planes, each couple of consecutive planes corresponding to a respective slice of the result of the 3D printing process. The method also comprises, for each couple of consecutive planes: obtaining one or more respective tool trajectories, determining a respective 2D contour corresponding to the one or more tool trajectories. The method also comprises determining a respective extrusion of the respective 2D contour bounded by a second plane of the couple and a first plane of the couple, and forming the boundary representation with the extrusions and portions of the planes. The method improves 3D printing.

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 simulating the machining of a workpiece with a cutting tool having at least one cutting part and at least one non-cutting part. The method comprises providing a set of dexels that represents the workpiece, a trajectory of the cutting tool, and a set of meshes each representing a respective cutting part or non-cutting part of the cutting tool. And then the method comprises for each dexel computing, for each mesh, the extremity points of all polylines that describe a time diagram, and testing a collision of the cutting tool with the workpiece along the dexel based on the lower envelope of the set of all polylines. Such a method improves the simulating of the machining of a workpiece.

Abstract: It is provided a computer-implemented method for designing a 3D modeled object, comprising providing, to a computer system, a NURBS surface that represents the 3D modeled object and that is defined by a grid of control points; determining (S20), by the computer system, a grid of surface points that belong to the NURBS surface, the grid of surface points corresponding to the grid of control points according to a predetermined invertible function; displaying, by the computer system, the NURBS surface and, on the NURBS surface, the grid of surface points; selecting, by graphical user-interaction, a subset of the surface points; modifying, by graphical user-interaction, position of the selected subset of surface points, and accordingly, updating real-time, by the computer system, the surface, the update being performed according to the predetermined invertible function. Such a method improves the design of a 3D modeled object.

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: 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 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: 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: 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.