A robot carrying a milling cutter or other multi-axis machine cuts a physical model and is directly driven in real time from a CAD generated mathematical model. The path planning is carried out in parametric space but with velocity constraints in the machine coordinate space. The method will generate proper points in parametric space and then map to machine space to minimize interpolations needed by machine controller to improve tracking accuracy while achieving the desired cutting velocity. Point data is computed by the microcomputer and transferred to the machine controller continuously while the machine is cutting. Long pre-cutting computation times are eliminated.