A Theoretically Complete Surface Segmentation Method for CNC Subtractive Fabrication

Abstract

We present a well improved surface segmentation algorithm for 3-axis/3+2-axis CNC subtractive fabrication. For a free-form surface (represented by the triangular mesh), to avoid collision with the cutter during complex surface machining, it is essential to segment it into several patches. We transform the surface segmentation problem into a mathematical problem based on energy minimization according to several fabrication constraints, and solved by establishing a weighted graph and searching the minimum cut. Our algorithm has simple structure and is easy to implement. Moreover, the algorithm guarantees correctness and completeness in theory, that is, we prove that the weight of the minimum cut is equivalent to the minimum value of the energy function. Experimental results are provided to illustrate and clarify our method.