The material removal and collision detection within MachineWorks software is based on creating boundary representations of the sweep of the tool, holder and machine parts as they move through space.
In the polygonal representation, each sweep is guaranteed to be within a specified chordal tolerance of the true surface. The 5-axis machining case alone took eight years of continuous software development to achieve optimal performance and accuracy.
In the RapidCut and Multicut software engines for die-mold simulation, sweeps are represented analytically so that where data is sampled the representation is accurate to double precision tolerances.