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 |
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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. (deposited 15 Oct 2022 21:00) [Currently Displayed]