Optimal Algorithms for Separating a Polyhedron from its Single-Part Mold Article Swipe
Prosenjit Bose
,
Tzvika Geft
,
Dan Halperin
,
Shahar Shamai
·
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.57717/cgt.v3i1.15
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.57717/cgt.v3i1.15
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 removed from the mold. We study the case where 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 removal direction. We give an O(n)-time algorithm that decides whether a given polyhedron with n facets is castable with a single-part mold. When possible, our algorithm provides an orientation of the polyhedron in the mold and a direction in which the product can be removed without breaking the mold. Moreover, we provide an optimal Θ(n log n)-time algorithm to compute all valid removal directions for polyhedra that are castable with a single-part mold. Both algorithms are an improvement by a linear factor over the previously best known algorithms for both of these problems. We also present an exact implementation of our algorithms using the CGAL library and employ our implementation to demonstrate the castability of a variety of polyhedra.
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Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/1708.04203
- OA Status
- green
- Cited By
- 1
- References
- 17
- Related Works
- 20
- OpenAlex ID
- https://openalex.org/W3167752317
All OpenAlex metadata
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https://openalex.org/W3167752317Canonical identifier for this work in OpenAlex
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https://doi.org/10.57717/cgt.v3i1.15Digital Object Identifier
- Title
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Optimal Algorithms for Separating a Polyhedron from its Single-Part MoldWork title
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preprintOpenAlex work type
- Language
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enPrimary language
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2022Year of publication
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2022-04-21Full publication date if available
- Authors
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Prosenjit Bose, Tzvika Geft, Dan Halperin, Shahar ShamaiList of authors in order
- Landing page
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https://arxiv.org/abs/1708.04203Publisher landing page
- Open access
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YesWhether a free full text is available
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greenOpen access status per OpenAlex
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https://arxiv.org/abs/1708.04203Direct OA link when available
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Mold, Polyhedron, Casting, Algorithm, Product (mathematics), Orientation (vector space), Object (grammar), Process (computing), Computer science, Engineering drawing, Mathematics, Materials science, Geometry, Composite material, Engineering, Artificial intelligence, Operating systemTop concepts (fields/topics) attached by OpenAlex
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1Total citation count in OpenAlex
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2021: 1Per-year citation counts (last 5 years)
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| referenced_works | https://openalex.org/W2000509570, https://openalex.org/W1481903970, https://openalex.org/W1981532073, https://openalex.org/W1986633330, https://openalex.org/W1990970199, https://openalex.org/W2098976733, https://openalex.org/W2103293229, https://openalex.org/W2079291191, https://openalex.org/W2047658650, https://openalex.org/W2086807633, https://openalex.org/W1996296982, https://openalex.org/W1993058867, https://openalex.org/W2025892728, https://openalex.org/W2021335272, https://openalex.org/W2963935545, https://openalex.org/W2059985428, https://openalex.org/W2080276023 |
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