Title data
Rambau, Jörg:
The visiblevolume function of a set of cameras is continuous, piecewise rational, locally Lipschitz, and semialgebraic in all dimensions.
In: Discrete & Computational Geometry.
Vol. 70
(12 August 2023)
.
 pp. 10381058.
ISSN 14320444
DOI: https://doi.org/10.1007/s0045402300541w
This is the latest version of this item.
Abstract in another language
The visiblevolume 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 visiblevolume function.
Earlier work has only considered this function in dimensions two and
three or for static environments implicitly defined by levelset
functions. In this paper it is shown, that the visiblevolume
function for a flexible environment modeled explicitly by a
parametrized simplicial complex is continuous, piecewise rational,
locally Lipschitz, and semialgebraic in all dimensions.
Further data
Item Type:  Article in a journal 

Refereed:  Yes 
Keywords:  visible volume; discrete geometry; semialgebraic 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:  02 Jul 2024 07:18 
Last Modified:  02 Jul 2024 07:18 
URI:  https://eref.unibayreuth.de/id/eprint/89883 
Available Versions of this Item

The visiblevolume function of a set of cameras is continuous, piecewise rational, locally Lipschitz, and semialgebraic in all dimensions. (deposited 15 Oct 2022 21:00)
 The visiblevolume function of a set of cameras is continuous, piecewise rational, locally Lipschitz, and semialgebraic in all dimensions. (deposited 02 Jul 2024 07:18) [Currently Displayed]