Three-axis ball end mills are used for the finishing of metal molds of complicated curved surfaces. Typically, a tool path of this shape machining is derived from the geometric calculations of a tool used, and a product model that is a computer aided design (CAD)-based polyhedron approximating the shape. The polyhedron is more complicated to approximate a shape with more curved surfaces, as it is highly time consuming. To solve this problem, methods to accelerate geometric calculations using a computer graphics drawing processing mechanism were proposed. However, these methods cannot guard against errors arising from the approximation of an inverse offset shape using a set of polygons. In the present study, we propose a method to generate tool paths accurately based on calculating the crossing points of the tool axis and defining the offset surface as a set of polygons, cylindrical surfaces, and spherical surfaces. With this method, it is expected that the height of an area, which was divided by fine polygons in previous methods, can be derived accurately, and a tool path can be generated with high precision.

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