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NAME
r.viewshed - Computes the viewshed of a point on an elevation raster map.
Default format: NULL (invisible), vertical angle wrt viewpoint (visible).
KEYWORDS
raster, viewshed, line of sight
SYNOPSIS
r.viewshed
r.viewshed --help
r.viewshed [-crbe] input=name output=name coordinates=east,north
[observer_elevation=value] [target_elevation=value] [max_distance=value]
[refraction_coeff=float] [memory=value] [directory=string] [--overwrite] [--help]
[--verbose] [--quiet] [--ui]
Flags:
-c
Consider the curvature of the earth (current ellipsoid)
-r
Consider the effect of atmospheric refraction
-b
Output format is invisible = 0, visible = 1
-e
Output format is invisible = NULL, else current elev - viewpoint_elev
--overwrite
Allow output files to overwrite existing files
--help
Print usage summary
--verbose
Verbose module output
--quiet
Quiet module output
--ui
Force launching GUI dialog
Parameters:
input=name [required]
Name of input elevation raster map
output=name [required]
Name for output raster map
coordinates=east,north [required]
Coordinates of viewing position
observer_elevation=value
Viewing elevation above the ground
Default: 1.75
target_elevation=value
Offset for target elevation above the ground
Default: 0.0
max_distance=value
Maximum visibility radius. By default infinity (-1)
Default: -1
refraction_coeff=float
Refraction coefficient
Options: 0.0-1.0
Default: 0.14286
memory=value
Amount of memory to use in MB
Default: 500
directory=string
Directory to hold temporary files (they can be large)
DESCRIPTION
r.viewshed is a module that computes the viewshed of a point on a raster terrain. That is,
given an elevation raster, and the location of an observer, it generates a raster output
map showing which cells are visible from the given location. The algorithm underlying
r.viewshed minimizes both the CPU operations and the transfer of data between main memory
and disk; as a result r.viewshed runs fast on very large rasters.
NOTES
To run r.viewshed, the user must specify an input elevation map name, an output raster map
name, and the location of the viewpoint.
For the time being the viewpoint (coordinates parameter) is assumed to be located inside
the terrain. The viewpoint location is given in map coordinates.
The output raster map may have one of three possible formats, based on which flags are
set.
By default, if no flag is set, the output is in angle-mode, and each point in the output
map is marked as NULL if the point is not visible or the respective point in the elevation
map is NULL. Otherwise, a value in [0, 180] representing the vertical angle with regard
to the viewpoint, in degrees, if the point is visible. A value of 0 is directly below the
specified viewing position, 90 is due horizontal. The angle to the cell containing the
viewing position is undefined and set to 180.
If the -b flag is set, the output is in boolean-mode, and each point in the output map is
marked as:
• 0 if the point is no-data/null or not visible
• 1 if the point is visible.
If the -e flag is set, the output is in elevation-mode, and each point in the output map
is marked as:
• no-data (null), if the respective point in the elevation map is no-data (null)
• -1, if the point is not visible
• the difference in elevation between the point and the viewpoint, if the point is
visible.
If you wish to identify the area of the map which is within the search radius but not
visible, a combination of r.buffer and r.mapcalc can be used to create a negative of the
viewshed map.
By default the elevations are not adjusted for the curvature of the earth. The user can
turn this on with flag -c.
By default the observer is assumed to have height 1.75 map units above the terrain. The
user can change this using option observer_elevation. The value entered is in the same
units as the elevation.
By default the target is assumed to have height of 0 map units above the terrain. The
user can change this using option target_elevation to determine if objects of a given
height would be visible. The value entered is in the same units as the elevation.
By default there is no restriction on the maximum distance to which the observer can see.
The user can set a maximum distance of visibility using option max_distance. The value
entered is in the same units as the cell size of the raster.
Main memory usage: By default r.viewshed assumes it has 500MB of main memory, and sets up
its internal data structures so that it does not require more than this amount of RAM.
The user can set the amount of memory used by the program by setting the memory_usage to
the number of MB of memory they would like to be used.
Memory mode
The algorithm can run in two modes: in internal memory, which means that it keeps all
necessary data structures in memory during the computation. And in external memory, which
means that the data structures are external, i.e. on disk. r.viewshed decides which mode
to run in using the amount of main memory specified by the user. The internal mode is
(much) faster than the external mode.
Ideally, the user should specify on the command line the amount of physical memory that is
free for the program to use. Underestimating the memory may result in r.viewshed running
in external mode instead of internal, which is slower. Overestimating the amount of free
memory may result in r.viewshed running in internal mode and using virtual memory, which
is slower than the external mode.
The algorithm
r.viewshed uses the following model for determining visibility: The height of a cell is
assumed to be variable, and the actual height of a point falling into a cell, but not
identical the cell center, is interpolated. Thus the terrain is viewed as a smooth
surface. Two points are visible to each other if their line-of-sight does not intersect
the terrain. The height for an arbitrary point x in the terrain is interpolated from the 4
surrounding neighbours. This means that this model does a bilinear interpolation of
heights. This model is suitable for both low and high resolution rasters as well as
terrain with flat and steep slopes.
The core of the algorithm is determining, for each cell, the line-of-sight and its
intersections with the cells in the terrain. For a (square) grid of n cells, there can be
O(n 1/2) cells that intersect the LOS. If we test every single such cell for every point
in the grid, this adds up to O(n3/2) tests. We can do all these tests faster if we re-use
information from one point to the next (two grid points that are close to each other will
be intersected by a lot of the same points) and organize the computation differently.
More precisely, the algorithm uses a technique called line sweeping: It considers a
half-line centered at the viewpoint, and rotates it radially around the viewpoint, 360
degrees. During the sweep it keeps track of all the cells that intersect the sweep line
at that time; These are called the active cells. A cell has 3 associated events: when it
is first met by the sweep line and inserted into the active structure; when it is last met
by the sweep line and deleted from the active structure; and when the sweep line passes
over its centerpoint, at which time its visibility is determined. To determine the
visibility of a cell all cells that intersect the line-of-sight must be active, so they
are in the active structure. The algorithm looks at all the active cells that are between
the point and the viewpoint, and finds the maximum gradient among these. If the cell’s
gradient is higher, it is marked as visible, whereas if it is lower, it is marked as
invisible.
For a (square) raster of n point in total, the standard viewshed algorithm uses O(n
sqrt(n))= O(n3/2) time, while the sweep-line algorithm uses O(n lg n) time. This
algorithm is efficient in terms of CPU operations and can be also made efficient in terms
of I/O-operations. For all details see the REFERENCES below.
The sweep-line. The active cells.
EXAMPLES
Using the North Carolina dataset: Compute viewshed from a observation point (coordinates:
638728.087167, 220609.261501) which is 5 meters above ground:
g.region raster=elev_lid792_1m -p
r.viewshed input=elev_lid792_1m output=elev_lid792_1m_viewshed \
coordinates=638728.087167,220609.261501 observer_elevation=5.0
Viewshed Using the Spearfish dataset: calculating the viewpoint from top of a mountain:
g.region raster=elevation.10m
r.viewshed input=elevation.10m output=viewshed \
coordinates=598869,4916642 mem=800
REFERENCES
• Computing Visibility on Terrains in External Memory. Herman Haverkort, Laura Toma
and Yi Zhuang. In ACM Journal on Experimental Algorithmics (JEA) 13 (2009).
• Computing Visibility on Terrains in External Memory. Herman Haverkort, Laura Toma
and Yi Zhuang. In the Proceedings of the 9th Workshop on Algorithm Engineering and
Experiments / Workshop on Analytic Algorithms and Combinatorics (ALENEX/ANALCO
2007).
SEE ALSO
r.mapcalc
AUTHORS
Laura Toma (Bowdoin College): ltoma@bowdoin.edu
Yi Zhuang (Carnegie-Mellon University): yzhuang@andrew.cmu.edu
William Richard (Bowdoin College): willster3021@gmail.com
Markus Metz
Last changed: $Date: 2014-12-19 22:55:37 +0100 (Fri, 19 Dec 2014) $
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