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r.viewshed(1grass) GRASS GIS User's Manual r.viewshed(1grass)

NAME
r.viewshed - Computes the viewshed of a point on an elevation raster
map.
Default format: NULL (invisible), vertical angle wrt viewpoint (visi-
ble).

KEYWORDS
raster, viewshed, line of sight, LOS

SYNOPSIS
r.viewshed
r.viewshed --help
r.viewshed [-crbe] input=name output=name coordinates=east,north [ob-
server_elevation=value] [target_elevation=value] [max_dis-
tance=value] [refraction_coeff=float] [memory=value] [direc-
tory=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 - view-
point_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 di-
rectly 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 view-
point, 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 en-
tered 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 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 compu-
tation. 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 inter-
polated. 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 interpo-
lated 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 radi-
ally 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 struc-
ture; 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 ac-
tive 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 algo-
rithm 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 oper-
ations 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=638728,220609 observer_elevation=5.0
Viewshed shown on shaded terrain (observer position in the north-east
quadrant with white dot; 5m above ground) 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 memory=800

REFERENCES
• Computing Visibility on Terrains in External Memory. Herman
Haverkort, Laura Toma and Yi Zhuang. In ACM Journal on Experi-
mental 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 / Work-
shop on Analytic Algorithms and Combinatorics (ALENEX/ANALCO
2007).