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 (S 10) 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 (S20), for each mesh, the extremity points of all polylines that describe a time ( h, t ) diagram, and testing (S30) 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.