Detecting collisions in a simulated machining of a workpiece represented by dexels

A method for producing a product, comprising:

• in a simulation phase, repeating implementation of simulating machining of a workpiece with a cutting tool having at least one cutting part and at least one non-cutting part;
• and
• providing after the simulation phase, a machining phase on the workpiece, wherein the simulating the machining being computer-implemented and comprising:
• providing:
• a set of dexels that represents the workpiece, each dexel having one or more segments, the one or more segments collectively representing the intersection between a line and the workpiece,
• a trajectory of the cutting tool, the trajectory of the cutting tool being a rigid motion, and
• a set of meshes each representing a respective cutting part or non-cutting part of the cutting tool;
• and then, for each dexel in the provided set:
• computing, for each mesh, the extremity points of all polylines that describe a time of intersection between the line of the dexel and the mesh as a function of a height of intersection, according to the trajectory of the cutting tool;
• and
• testing a collision of the cutting tool with the workpiece along the dexel, wherein the testing includes determining if, for a value of height that corresponds to a position that belongs to a lower envelope of the set of all polylines of all meshes, the polyline to which the position belongs being associated to a non-cutting part, the value of height belongs to one of the segments of the dexel.

A computer program product comprising:

• a non-transitory computer readable storage medium having recorded thereon a data structure including specifications of a simulation of machining of a workpiece with a cutting tool having at least one cutting part and at least one non-cutting part;
• and
• computer-implemented simulation instructions carried on the computer readable storage medium including instructions for:
• providing to a machining simulation:
• a set of dexels that represents the workpiece, each dexel having one or more segments, the one or more segments collectively representing the intersection between a line and the workpiece,
• a trajectory of the cutting tool, the trajectory of the cutting tool being a rigid motion, and
• a set of meshes each representing a respective cutting part or non-cutting part of the cutting tool;
• and then, for each dexel in the provided set:
• computing, for each mesh, the extremity points of all polylines that describe a time of intersection between the line of the dexel and the mesh as a function of a height of intersection, according to the trajectory of the cutting tool;
• and
• testing a collision of the cutting tool with the workpiece along the dexel, wherein the testing includes determining if, for a value of height that corresponds to a position that belongs to a lower envelope of the set of all polylines of all meshes, the polyline to which the position belongs being associated to a non-cutting part, the value of height belongs to one of the segments of the dexel.

A system comprising:

• a processor coupled to a memory;
• the memory having recorded thereon instructions for performing a computer-implemented simulating of machining of a workpiece with a cutting tool having at least one cutting part and at least one non-cutting part, the instructions comprising:
• providing to a machining simulation:
• a set of dexels that represents the workpiece, each dexel having one or more segments, the one or more segments collectively representing the intersection between a line and the workpiece,
• a trajectory of the cutting tool, the trajectory of the cutting tool being a rigid motion, and
• a set of meshes each representing a respective cutting part or non-cutting part of the cutting tool;
• and then, for each dexel in the provided set:
• computing, for each mesh, the extremity points of all polylines that describe a time of intersection between the line of the dexel and the mesh as a function of a height of intersection, according to the trajectory of the cutting tool;
• and
• testing a collision of the cutting tool with the workpiece along the dexel, wherein the testing includes determining if, for a value of height that corresponds to a position that belongs to a lower envelope of the set of all polylines of all meshes, the polyline to which the position belongs being associated to a non-cutting part, the value of height belongs to one of the segments of the dexel.

A non-transitory computer readable storage medium comprising:

• a computer program recorded thereon and having instructions for performing a computer-implemented simulation of machining of a workpiece with a cutting tool, the cutting tool formed of at least one cutting part and at least one non-cutting part,
• the instructions comprising:
• providing to a machining simulation:
• a set of dexels that represents the workpiece, each dexel having one or more segments, the one or more segments collectively representing the intersection between a line and the workpiece,
• a trajectory of the cutting tool, the trajectory of the cutting tool being a rigid motion, and
• a set of meshes each representing a respective cutting part or non-cutting part of the cutting tool;
• and then, for each dexel in the provided set:
• computing, for each mesh, the extremity points of all polylines that describe a time of intersection between the line of the dexel and the mesh as a function of a height of intersection, according to the trajectory of the cutting tool;
• and
• testing a collision of the cutting tool with the workpiece along the dexel, wherein the testing includes determining if, for a value of height that corresponds to a position that belongs to a lower envelope of the set of all polylines of all meshes, the polyline to which the position belongs being associated to a non-cutting part, the value of height belongs to one of the segments of the dexel.