Volume 4, Issue 2
A Theoretically Complete Surface Segmentation Method for CNC Subtractive Fabrication

CSIAM Trans. Appl. Math., 4 (2023), pp. 325-344.

Published online: 2023-02

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• 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.

68U05, 68U07, 05C90

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@Article{CSIAM-AM-4-325, author = {Ma , Hong-YuYuan , Chun-MingShen , Li-Yong and Feng , Yi-Fei}, title = {A Theoretically Complete Surface Segmentation Method for CNC Subtractive Fabrication}, journal = {CSIAM Transactions on Applied Mathematics}, year = {2023}, volume = {4}, number = {2}, pages = {325--344}, 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.

}, issn = {2708-0579}, doi = {https://doi.org/10.4208/csiam-am.SO-2022-0032}, url = {http://global-sci.org/intro/article_detail/csiam-am/21417.html} }
TY - JOUR T1 - A Theoretically Complete Surface Segmentation Method for CNC Subtractive Fabrication AU - Ma , Hong-Yu AU - Yuan , Chun-Ming AU - Shen , Li-Yong AU - Feng , Yi-Fei JO - CSIAM Transactions on Applied Mathematics VL - 2 SP - 325 EP - 344 PY - 2023 DA - 2023/02 SN - 4 DO - http://doi.org/10.4208/csiam-am.SO-2022-0032 UR - https://global-sci.org/intro/article_detail/csiam-am/21417.html KW - Surface segmentation, triangular mesh model, minimum cut, subtractive fabrication. AB -

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.

Hong-Yu Ma, Chun-Ming Yuan, Li-Yong Shen & Yi-Fei Feng. (2023). A Theoretically Complete Surface Segmentation Method for CNC Subtractive Fabrication. CSIAM Transactions on Applied Mathematics. 4 (2). 325-344. doi:10.4208/csiam-am.SO-2022-0032
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