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Convex Partitions of Polyhedra: A Lower Bound and Worst-Case Optimal Algorithm
Abstract
The problem of partitioning a polyhedron into a minimum number of convex pieces is known to be NP-hard. We establish here a quadratic lower bound on the complexity of this problem, and we describe an algorithm that produces a number of convex parts within a constant factor of optimal in the worst case. The algorithm is linear in the size of the polyhedron and cubic in the number of reflex angles. Since in most applications areas, the former quantity greatly exceeds the latter, the algorithm is viable in practice.
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Citations
Cited by
Accurate and Fast Proximity Queries Between Polyhedra Using Convex Surface Decomposition
Ehmann, S. A., & Lin, M. C. (2001) · Computer Graphics Forum · doi:10.1111/1467-8659.00543 · Cited by 264
Approximate convex decomposition for 3D meshes with collision-aware concavity and tree search
Wei, X., Liu, M., Ling, Z., & Su, H. (2022) · ACM Transactions on Graphics · doi:10.1145/3528223.3530103 · Cited by 80
Metadata
- Authors
- Chazelle, B.
- Venue
- SIAM Journal on Computing
- Published
- 1984-08
- Volume
- 13
- Issue
- 3
- Pages
- 488-507
- ISSN
- 0097-5397 (ISSN-L)
- 1095-7111
- OpenAlex
- W2045155153
- Cited by
- 238
- References
- 0
- FWCI
- 3.10
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: Convex Partitions of Polyhedra: A Lower Bound and Worst-Case Optimal Algorithm. https://app.cochat.ai/papers/10.1137/0213031
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- Chazelle, B. (1984). Convex Partitions of Polyhedra: A Lower Bound and Worst-Case Optimal Algorithm. SIAM Journal on Computing. https://doi.org/10.1137/0213031
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
