The work describes an innovative method with which to calculate the visibility [61, 62]
and Fresnel zones on digital maps using graphics processing NVIDIA CUDA cards. Three
parallel algorithms were formulated:
• modified R2 parallel algorithm for calculating visibility (R2-P),
• algorithm for calculating Fresnel zone clearance (FZC),
• algorithm for calculating Fresnel zone transverse intersection between the transmitter
and the receiver (FZTI).
The R2 parallel algorithm was developed based on the established R2 sequential algorithm
for computing visibility. Aside from threading, other useful features of the graphics
processing unit were used to speed up calculation time. Coalesced access to the global
memory helps speed up the flow of information and thus also speeds up the calculation.
Exchange of information between threads during computation plays a key role in the
speedup. The segmentation of the digital map enables the calculation of visibility for
huge data sets.
The modified parallel R2 algorithm was compared with the already implemented algorithms
for the viewshed calculation in term of accuracy and duration of the calculation.
It turned out that the new algorithm R2-P had the same accuracy as the already established
sequential algorithm R2, although the former also makes it possible to significantly
speed up the calculation. Calculation time is reduced from the order of a few minutes to
the order of a couple of seconds. This, in practice, means that there is a possibility of
In addition to the viewshed, Fresnel zone clearance is very useful for planning the radio
coverage. Algorithm FZC starts with the location of the radio transmitter, the height of
the transmitter, the receiver observation height above terrain, and the wavelength of
the radio waves. The algorithm for each point of the terrain calculates the first clear
Fresnel zone. The result is a digital map with the plotted areas of Fresnel zone clearance.
This map provides better information about the radio signal than just a calculation of the
viewshed. Indeed areas where the first Fresnel zone is completely obscured are particularly
good for providing very useful information. The algorithm also has the ability to take
into account land use, where the height of the terrain is raised as a function of land use
(eg. For the forest area, raising can be 15 m).
With modifications, such as the introduction of the Friis transmission equation and
consideration of the radiation pattern, the algorithm becomes a simple radio propagation
model and thus is suitable for the calculation of radio coverage. Calculation of the radio
propagation is compared with the measured values on a field for frequencies of 90 MHz
(FM), 800 MHz (LTE) and 1800 MHz (LTE). For a variety of input parameters, the
standard deviation of changes between the field measurements and calculated propagation
is presented in graphs. In this way, the optimal values of the input parameters for each
frequency band can be obtained.
The algorithm for calculating Fresnel zone transverse intersection between the transmitter
and the receiver produces an image of Fresnel zones, which represents the mathematical
section of all scale cross-sectional Fresnel zones along the transmission path. The
result is a visual image that shows the characteristics of the radio link in terms of masking
individual Fresnel zones. In practice, the algorithm is most useful in the design of radio
links, where man can check how much and which part of the Fresnel zone is missing due
to terrain obstacles.
All three algorithms were implemented as GRASS GIS modules and can be used on any
PC with an integrated GPU NVIDIA CUDA and loaded with the appropriate free-access