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Compoundly weighted Voronoi: a sequential and parallel implementation

Vincent Boerjan
Universiteit Hasselt
Universiteit Hasselt, 2014

@article{boerjan2014compoundly,

   title={Compoundly weighted Voronoi: a sequential and parallel implementation},

   author={Boerjan, Vincent},

   year={2014},

   publisher={UHasselt}

}

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SMARAD is the Smart and Novel Radios research unit at Aalto University in Helsinki. In the context of their smart radio research the area of influence of existing television transmitters is important data for the placement of experimental transmitters. Currently these areas are calculated with a regular Voronoi tessellation ignoring variation in transmitter characteristics. This thesis offers a more accurate generalised Voronoi implementation. In this thesis the optimal construction method for a regional division with given characteristics is selected and implemented. This results in three different versions with a similar algorithm but on different platforms: Matlab, C and OpenCL. The Matlab version is the slowest but includes an additional API to map the result automatically to a topographic map of the target region using an internet source. The other implementations require an input image with the correct dimensions defined by the user to achieve the same results. The fastest implementation is the OpenCL version; however, cross-platform compatibility is limited. In this thesis the adaptive nature of the algorithm is also demonstrated by implementing different generalisations of the Voronoi tessellation to achieve a more accurate result for a given real world scenario. The knowledge gathered from this thesis has applications for region division in signal processing as well as other scientific fields given the adaptive nature of the code. Examples of possible use include cellular and crystal growth, computer generated graphics and computational geometry.
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