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Voronoi diagrams – inventor, method, applications

Pokojski W., Pokojska P.

Polish Cartographical Review

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2018

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Vol. 50, No. 3

141--150

EN

The article presents the person and works of Georgy Voronoi (1868–1908), the inventor of an original method of diagrams, a student of the famous mathematician Andrey Markov. Georgy Voronoi graduated from the Department of Physics and Mathematics at the University of St. Petersburg, and subsequently worked as a professor of mathematics at the Imperial University of Warsaw. One of his students was the future outstanding Polish mathematician Wacław Sierpiński. In his brief lifetime G. Voronoi published several important scientific articles on number theory. In an almost 100 page paper in French published in 1908 he described a method of diagrams, or polygons, which became known as the method of Voronoi diagrams. In the digital age this method and its modifications found new applications. The entry “Voronoi” is getting more popular on the Internet, and the method of Voronoi diagrams and its modifications are widely described in handbooks and scientific articles. The article presents application of the method in the most popular computer programs from the Geographic Information System (GIS) group and presents examples of its usage in research on geographic space in various scientific disciplines.

2

Modelowanie struktury przestrzennej elementów bilansu wodnego (na przykładzie dorzecza Regi)

Pokojska P.

Przegląd Geofizyczny

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2001

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Z. 1-2

15-35

EN

The aim of the research is simulation of spatial distribution of water balance elements: actual evapotranspiration, surface runoff and groundwater recharge, in catchment representing mesoscale, with use of distributed parameters model WetSpass. Model was applied in Rega basin in 5-year periods and 40-year period 1956-1995. Numerical maps of hydrological and meteorological elements and physiographic features were prepared with use of GIS technics; optimal size of elementary field was determined on each input map to the model. Results of the verification of the model in 5-year periods and 40-year period, made in three hydrometric gauges in the catchment were good. Spatial distribution of mean annual values of actual evapotranspiration, surface runoff and groundwater recharge in 40-year period 1956-1995 was analysed and described.

3

Skutki awarii rurociągu solankowego Góra - Mątwy i metody przeciwdziałania degradacji gleb

Hulisz P., Pokojska P., Posadzy P.

Inżynieria Ekologiczna

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2001

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Nr 5

63--69

PL

Badaniami objęto gleby będące pod wpływem niedawnych awarii rurociągu solankowego Góra - Mątwy. Ogromne stężenia NaCI w nasyconym ekstrakcie glebowym, dochodzące do 1/3 stężenia solanki spowodowały zniszczenie pokrywy roślinnej i naturalnej struktury gleby oraz zmniejszenie zdolności przesiąkania roztworów. Głównymi przyczynami awarii są zewnętrzna korozja elektrolityczna rurociągu oraz zła jakość wykonawstwa. Rekultywacja gleb zdegradowanych wyciekami solanki nie może zastąpić działań zmierzających do całkowitej likwidacji źródła skażenia tj. wymiany rur.

EN

The studies were carried out in soils influenced by recent the Góra - Mątwy brine pipeline damages. The very high concentrations of NaCI in saturation extract (up to 1/3 of brine concentration) caused the damage of the plant cover, the destruction of the soil natural structure and the decrease of the soil permeability. The main reasons of the brine pipeline damages are external electrolytical corrosion of the pipeline and bad quality of the construction. The reclamation of degraded soils gives good results, but it necessary to liquidate the pollution source by the replacement of pipes system.

4

Model hydrologiczny o parametrach przestrzennie rozłożonych, zintegrowany z Systemem Informacji Geograficznej

Pokojska P.

Przegląd Geofizyczny

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2000

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Z. 3-4

299-308

EN

The aim of the article is presentation of spatially distributed water balance model WetSpass, inte-grated into Geographical Information Systems, developed in Free University of Brussels. Model simulates average spatial pattern of actual evapotranspiration, surface runoff and groundwater re-charge in raster cells. Model purposes, its structure, parameters and verification results have been described on the basis of selected publications.