max planck institut
informatik

# MPI-I-92-102

## Maintaining the visibility map of spheres while moving the viewpoint on a circle at infinity

### Lenhof, Hans-Peter and Smid, Michiel

MPI-I-92-102. January 1992, 16 pages. | Status: available - back from printing | Next --> Entry | Previous <-- Entry

Abstract in LaTeX format:
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.
Acknowledgement:
References to related material:

92-102.pdf45769 KBytes
Please note: If you don't have a viewer for PostScript on your platform, try to install GhostScript and GhostView
URL to this document: http://domino.mpi-inf.mpg.de/internet/reports.nsf/NumberView/1992-102
BibTeX
@TECHREPORT{LenhofSmid92a,
AUTHOR = {Lenhof, Hans-Peter and Smid, Michiel},
TITLE = {Maintaining the visibility map of spheres while moving the viewpoint on a circle at infinity},
TYPE = {Research Report},
INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},