Fig. 1. Iso-planar (Cartesian) tool path generation.

Fig. 2. (a) Consecutive tool paths with ball–ball intersection. (b) Consecutive tool paths with ball–cylinder intersection.

Fig. 3. (a) Applying plane–surface intersection. (b) Plane–surface intersection curves. (c) Cutter contact (CC) tool paths. (d) Redundant tool paths in associated flatter regions.

Fig. 4. Isophotes and light regions.

Fig. 5. (a) Isoline intersects a horizontal grid line. (b) Isoline intersects a vertical grid line. (c) Isoline intersects a horizontal and a vertical grid line.

Fig. 6. Two isolines are in one grid.

Fig. 7. (a) Light regions on piecewise C² continuous surfaces. (b) A union light region on piecewise C² continuous surfaces.

Fig. 8. Points inside and outside a close region.

Fig. 9. (a) Tool paths in light region and associated flatter regions in xy plane. (b) The change of light region and tool paths in xy plane.

Fig. 10. Global and local tool paths.

Fig. 11. Plane intervals of global–local tool paths. (a) One local tool path. (b) Two local tool paths.

Fig. 12. (a) Light region boundaries on a free-form surface. (b) Zigzag tool paths generated by iso-planar algorithm. (c) Zigzag tool paths outside light regions. (d) Zigzag tool paths inside light regions.

Fig. 13. Tool paths generated with global–local strategy.

Fig. 14. (a) Light region boundaries on a composite surface. (b) Uni-direction tool paths generated by iso-planar algorithm. (c) Uni-direction tool paths outside light regions. (d) Uni-direction tool paths inside light regions.

Table 1. Tool path length comparison for Example 1 (unit: mm)

Table 2. Tool path length comparison for Example 2 (unit: mm)

Table 3. Tool path length comparison for Example 3 (unit: mm)