@techreport{LenhofSmid92a,
TITLE = {Maintaining the visibility map of spheres while moving the viewpoint on a circle at infinity},
AUTHOR = {Lenhof, Hans-Peter and Smid, Michiel},
LANGUAGE = {eng},
NUMBER = {MPI-I-92-102},
INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
ADDRESS = {Saarbr{\"u}cken},
YEAR = {1992},
DATE = {1992},
ABSTRACT = {We investigate 3D visibility problems for scenes that consist of $n$ non-intersecting spheres. The viewing point $v$ moves on a flightpath that is part of a ``circle at infinity'' given by a plane $P$ and a range of angles $\{\alpha(t)|t\in [0:1]\}\subset [0:2\pi]$. At ``time'' $t$, the lines of sight are parallel to the ray $r(t)$ in the plane $P$, which starts in the origin of $P$ and represents the angle $\alpha(t)$ (orthographic views of the scene). We describe algorithms that compute the visibility graph at the start of the flight, all time parameters $t$ at which the topology of the scene changes, and the corresponding topology changes. We present an algorithm with running time $O((n+k+p)\log n)$, where $n$ is the number of spheres in the scene; $p$ is the number of transparent topology changes (the number of different scene topologies visible along the flightpath, assuming that all spheres are transparent); and $k$ denotes the number of vertices (conflicts) which are in the (transparent) visibility graph at the start and do not disappear during the flight.},
TYPE = {Research Report / Max-Planck-Institut für Informatik},
}