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

DOI zum Zitieren der Version auf EPub Bayreuth: https://doi.org/10.15495/EPub_UBT_00006709
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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