## 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.