Engagement milling

1. A method for generating a spiral-like tool path for milling a region of a workpiece, the method comprising the steps of:

creating a family of concentric indexed circular arcs at each of two or more separate and distinct selected points within the region;

determining, using a computer, parameters of a first set of blends to connect together the circular arcs of adjacent families of the circular arcs having an identical index to form a plurality of isoloops;

determining, using a computer, parameters of a second set of blends for blending between adjacent isoloops to form the spiral-like tool path, and

generating instructions for controlling a milling cutter to mill the region in accordance with the generated spiral-like tool path.

2. The method of claim 1 , wherein a radius of each concentric arc, the parameters of each first set of blends and the parameters of each second set of blends are selected such that an engagement of the milling cutter following the tool path does not exceed a predetermined value of cutter engagement.

3. The method of claim 1 , wherein a radius of each concentric arc, the parameters of each first set of blends and the parameters of each second set of blends are selected such that an engagement of the milling cutter following the tool path substantially equals a predetermined value of cutter engagement.

4. The method of claim 1 , wherein the selected points lay on a medial axis of the region.

5. The method of claim 4 , wherein the locations of branch points on the medial axis are determined using the medial axis transform.

6. The method of claim 1 , wherein a largest circular arc in each family of concentric circular arcs is tangent to three sides of the region.

7. A non-transitory computer readable storage medium for having an executable program for generating a spiral-like tool path for milling a region of a workpiece stored thereon, wherein the program instructs a computer to perform the steps of:

creating a family of concentric indexed circular arcs at each of two or more separate and distinct selected points within the region;

determining parameters of a first set of blends to connect together the circular arcs of adjacent families of the circular arcs having an identical index to form a plurality of isoloops;

determining, parameters of a second set of blends for blending between adjacent isoloops to form the spiral-like tool path, and

generating instructions for controlling a milling cutter to mill the region in accordance with the generated spiral-like tool path.

8. The non-transitory computer readable storage medium of claim 7 , wherein a radius of each concentric arc, the parameters of each first set of blends and the parameters of each second set of blends are selected such that an engagement of the milling cutter following the tool path does not exceed a predetermined value of cutter engagement.

9. The non-transitory computer readable storage medium of claim 7 , wherein a radius of each concentric arc, the parameters of each first set of blends and the parameters of each second set of blends are selected such that an engagement of the milling cutter following the tool path substantially equals a predetermined value of cutter engagement.

10. The non-transitory computer readable storage medium of claim 7 , wherein the selected points lay on a medial axis of the region.

11. The non-transitory computer readable storage medium of claim 10 , wherein the locations of branch points on the medial axis are determined using the medial axis transform.

12. The non-transitory computer readable storage medium of claim 7 , wherein a largest circular arc in each family of concentric circular arcs is tangent to three sides of the region.

13. A machine for generating a spiral-like tool path for milling a region of a workpiece comprising:

a computer coupled to a memory, wherein the computer is programmed to generate the tool path by the steps of:

creating a family of concentric indexed circular arcs at each of two or more separate and distinct selected points within the region;

determining parameters of a first set of blends to connect together the circular arcs of adjacent families of the circular arcs having an identical index to form a plurality of isoloops;

determining, parameters of a second set of blends for blending between adjacent isoloops to form the spiral-like tool path, and

generating instructions for controlling a milling cutter to mill the region in accordance with the generated spiral-like tool path.

14. The machine of claim 13 , wherein a radius of each concentric arc, the parameters of each first set of blends and the parameters of each second set of blends are selected such that an engagement of the milling cutter following the tool path does not exceed a predetermined value of cutter engagement.

15. The machine of claim 13 , wherein a radius of each concentric arc, the parameters of each first set of blends and the parameters of each second set of blends are selected such that an engagement of the milling cutter following the tool path substantially equals a predetermined value of cutter engagement.

16. The machine of claim 13 , wherein the selected points lay on a medial axis of the region.

17. The machine of claim 16 , wherein the locations of branch points on the medial axis are determined using the medial axis transform.

18. The machine of claim 13 , wherein a largest circular arc in each family of concentric circular arcs is tangent to three sides of the region.