## Title data

Rambau, Jörg:

**The visible-volume function of a set of cameras is continuous, piecewise rational, locally Lipschitz, and semi-algebraic in all dimensions.**

Lehrstuhl Wirtschaftsmathematik, University of Bayreuth

Bayreuth
,
2022
. - 19 p.

DOI: https://doi.org/10.15495/EPub_UBT_00006709

## Abstract in another language

The visible-volume function assigns to a configuration of cameras

and a flexible environment in a convex room the volume that can be

supervised by the cameras. It is of interest to configure the

cameras and the environment in such a way that the visible volume is

maximized. Some methods of global optimization can take profit from

desirable analytic properties of the visible-volume function.

Earlier work has only considered this function in dimensions two and

three or for static environments implicitly defined by level-set

functions. In this paper it is shown, that the visible-volume

function for a flexible environment modeled explicitly by a

parametrized simplicial complex is continuous, piecewise rational,

locally Lipschitz, and semi-algebraic in all dimensions.

## Further data

Item Type: | Preprint, postprint |
---|---|

Additional notes: | Erscheint in: Discrete & Computational Geometry |

Keywords: | visible volume; discrete geometry; semi-algebraic sets; hyperplane arrangements; point configurations; oriented matroids; triangulations; piecewise rational; locally Lipschitz |

Subject classification: | MSC 52C35, MSC 52C40, MSC 68U05 |

Institutions of the University: | Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematical Economics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematical Economics > Chair Mathematical Economics - Univ.-Prof. Dr. Jörg Rambau Faculties Faculties > Faculty of Mathematics, Physics und Computer Science |

Result of work at the UBT: | Yes |

DDC Subjects: | 500 Science > 510 Mathematics |

Date Deposited: | 15 Oct 2022 21:00 |

Last Modified: | 17 Oct 2022 05:36 |

URI: | https://eref.uni-bayreuth.de/id/eprint/72445 |