Analytical computer-aided machining system and method

A method as in claim 10 wherein he step of calculating the actual tool control point curve includes steps comprising:

• (1) when a segment of the approximate tool control point curve between a pair of actual tool control points is not within tolerance of the mathematical representation, then calculating an intermediate actual tool control point;
• (2) testing the tolerance of the tool control point curve between the intermediate actual tool control point and one of the pair of actual tool control points;
• repeating steps (1) and (2) above if the tool control point curve is not within tolerance;
• testing the tolerance of the tool control point curve between the intermediate point and the other of the pair of actual tool control points;
• and
• repeating steps (1) and (2) above if the tool control point curve is not within tolerance.

A method for controlling a machine tool to mill a surface of a part having a known mathematical representation, the method comprising:

• using the known mathematical representation, calculating an approximate offset surface of the surface to be milled;
• calculating the location of points on the offset surface which points are furthest in and opposite a direction in which a cut is to occur;
• calculating coordinates of a plane through the point furthest opposite the direction of the cut;
• calculating a tool control point curve for the cut using the intersection of the plane with the offset surface;
• and
• supplying a numerical representation of the tool control point curve for use by apparatus for controlling the machine tool to move over a portion of the tool control point curve.