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On the Separation of a Polyhedron from Its Single-Part Mold

Abstract

Casting is a manufacturing process where liquid material is poured into a mold having the shape of a desired product. After the material solidifies, the product is pulled out of the mold. We study the case in which the mold is made of a single part and the object to be produced is a three-dimensional polyhedron. Objects that can be produced this way are called castable with a single-part mold. A direction in which the object can be removed without breaking the mold is called a valid pull-out direction. We give an algorithm that decides whether a given polyhedron with \(n\) facets is castable with a single-part mold, and if so indicates how to orient the polyhedron in the mold and a direction in which the product can be pulled out without breaking the mold. Our algorithm runs in \(O(n)\) time. The best previously known algorithm for this problem runs in \(O<(n^2)\) time.

Links

  • Shahar ShamaiDan Halperin, and Prosenjit Bose
    On the Separation of a Polyhedron from Its Single-Part Mold
    In proceedings of the 13th Conference on Automation Science and Engineering (CASE), 2017 [link][bibtex]
    arXiv:1708.04203v2 [link][bibtex]
  • Prosenjit Bose, Efi Fogel, Tzvika Geft, Dan Halperin, and Shahar Shamai
    Optimal Algorithms for Separating a Polyhedron from its Single-Part Mold
    Computing in Geometry and Topology, 3(1): 7:1–7:19, 2024 [link][bibtex]

Contacts

Shahar Shamai
Dan Halperin
Prosenjit Bose
@article{bfghs-oaspf-24,
  author       = {Prosenjit Bose and Efi Fogel and Tzvika Geft and Dan Halperin and Shahar Shamai},
  title        = {Optimal Algorithms for Separating a Polyhedron from its Single-Part Mold},
  volume       = {3},
  doi          = {10.57717/cgt.v3i1.15},
  number       = {1},
  journal      = {Computing in Geometry and Topology},
  year         = {2024},
  pages        = {7:1--7:19}
}
@article{sh-spfsp-17,
  author       = {Prosenjit Bose and Dan Halperin and Shahar Shamai},
  title        = {On the Separation of a Polyhedron from Its Single-Part Mold},
  journal      = {CoRR},
  volume       = {abs/1708.04203},
  year         = {2017},
  url          = {http://arxiv.org/abs/1708.04203},
  eprinttype   = {arXiv},
  eprint       = {1708.04203},
  timestamp    = {Mon, 13 Aug 2018 16:48:58 +0200},
  biburl       = {https://dblp.org/rec/journals/corr/abs-1708-04203.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{sh-spfsp-17,
  author = {Shahar Shamai and Dan Halperin and Prosenjit Bose},
  booktitle = {Proceedings of the 13th IEEE Conference on Automation Science and Engineering (CASE)}, 
  title = {On the separation of a polyhedron from its single-part mold}, 
  year = {2017},
  pages = {61--66},
  doi = {10.1109/COASE.2017.8256076}
}

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