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

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##### Fulltext (public)

92-102.pdf

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##### Supplementary Material (public)

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##### Citation

Lenhof, H.-P., & Smid, M.(1992). *Maintaining the visibility
map of spheres while moving the viewpoint on a circle at infinity* (MPI-I-92-102). Saarbrücken: Max-Planck-Institut
für Informatik.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0014-B059-2

##### 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.