The present invention relates to a curve-based method for generating NC machining paths of a polyhedron model. The present invention relates to a process of assigning topological properties to a polyhedron model that satisfies the vertex sharing rule and has only geometrical properties, and uses topological relationships of edges and vertices. The process of defining geometric characteristics (convex, concave, flat, saddle), the accurate representation of triangular, triangular, cylindrical and spherical trimming surfaces created from triangular, convex edges or vertices, It is possible to calculate accurate CL path data stably and quickly by finding the intersection between possible drive planes and rearranging, trimming, and connecting the curves and segments generated after slicing.
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