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 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 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: 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.