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URN to cite this document: urn:nbn:de:bvb:703-epub-6709-4
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 S.
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Abstract
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 (visible to public): | 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 |
| DDC Subjects: | 500 Science > 510 Mathematics |
| 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 |
| Language: | English |
| Originates at UBT: | Yes |
| URN: | urn:nbn:de:bvb:703-epub-6709-4 |
| Date Deposited: | 10 Oct 2022 13:00 |
| Last Modified: | 10 Oct 2022 13:00 |
| URI: | https://epub.uni-bayreuth.de/id/eprint/6709 |
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