{"id":31223732,"url":"https://github.com/mit-acl/minvo","last_synced_at":"2025-09-21T22:55:38.580Z","repository":{"id":41553098,"uuid":"286563106","full_name":"mit-acl/minvo","owner":"mit-acl","description":"Simplexes with Minimum Volume Enclosing Polynomial 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MINVO Basis: Finding Simplexes with Minimum Volume Enclosing Polynomial Curves #\n\nExample for n=3:\n\n[![](./imgs/minvo3d.png)](https://www.youtube.com/watch?v=x5ORkDCe4O0) \n\nMINVO roots:\n\n[![](./imgs/MINVO_roots.png)](https://www.youtube.com/watch?v=x5ORkDCe4O0) \n\n## Citation\n\nWhen using MINVO, please cite this paper ([pdf](https://arxiv.org/abs/2010.10726), [video](https://youtu.be/x5ORkDCe4O0)):\n\n```bibtex\n@article{tordesillas2022minvo,\n  title={MINVO Basis: Finding Simplexes with Minimum Volume Enclosing Polynomial Curves},\n  author={Tordesillas, Jesus and How, Jonathan P},\n  journal={Computer-Aided Design},\n  volume={151},\n  pages={103341},\n  year={2022},\n  publisher={Elsevier}\n}\n```\n\n## Instructions to use the MINVO basis\n\n* **For a particular curve (Problem 1 of the paper)**: See an example (with `n=3`) in [`curve_given3D.m`](https://github.com/mit-acl/minvo/blob/master/src/curve_given3D.m)\n\n* **For a particular simplex  (Problem 2 of the paper)**: See an example (with `n=3`) in [`simplex_given3D.m`](https://github.com/mit-acl/minvo/blob/master/src/simplex_given3D.m)\n\nTo obtain all the figures of the paper, you can  simply run [`plot_solution.m`](https://github.com/mit-acl/minvo/blob/master/src/plot_solution.m) \n\nYou don't need to install any external solvers for the steps above.\n\n## Instructions to derive the MINVO basis\n\n* The file [`general_formulation_sos.m`](https://github.com/mit-acl/minvo/blob/master/src/general_formulation_sos.m) solves Problem 3 in the paper using SOS.\n* The file [`general_formulation_lukacs_theorem.m`](https://github.com/mit-acl/minvo/blob/master/src/general_formulation_lukacs_theorem.m) solves Problem 3 in the paper using the Markov–Lukács Theorem. \n* The file [`formula_formulation.m`](https://github.com/mit-acl/minvo/blob/master/src/formula_formulation.m) solves Problem 4 in the paper. \n\nFollow the instructions in each file to prove local/global optimality.\n\nDepending on the settings you choose in each file, you may need to install [YALMIP](https://yalmip.github.io/) (tested with [this release](https://github.com/yalmip/YALMIP/releases/tag/R20200116_hotfix)), [SNOPT](https://ccom.ucsd.edu/~optimizers/) and/or [MOSEK](https://www.mosek.com/). \n\n\n---------\n\n\u003e **Approval for release**: This code was approved for release by The Boeing Company in December 2020. \n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fmit-acl%2Fminvo","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fmit-acl%2Fminvo","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fmit-acl%2Fminvo/lists"}