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Voronoi cell constructions on the map
Čermák, Jan ; Hrdina, Jaroslav (referee) ; Pavlík, Jan (advisor)
This bachelor’s thesis deals with study of Voronoi cell and its representation in Voronoi diagrams and their construction on the model of Earth’s surface. At first, Voronoi diagrams and their characteristics are explained in a plane, we describe their construction using Fortune’s algorithm, then spherical geometry is explained. Then we take a look at some equations that are useful for calculating on a sphere, and we use them for calculating distances on Earth, which we approximate with a sphere. Finally we apply Fortune’s algorithm on a sphere, we explain the principles of construction of Voronoi diagrams with this algorithm on a sphere and changes compared to the planar case that must be taken care of. The goal of the thesis is to display Voronoi diagram on Google maps, thus we work with Google Maps API.
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Spherical geometry
Kokh, Konstantin ; Vašík, Petr (referee) ; Doupovec, Miroslav (advisor)
This bachelor thesis deals with the description of sphere and spherical geometry. The second chapter defines the mathematical apparatus that we will need in the next part of the work. The third part begins with describing the sphere from the point of view of differential geometry of curves and planes. In the middle, we will show the conformal map of the sphere to the plane and the equiareal map of the sphere to the cylinder. Then we will describe the basic properties of spherical geometry. In the end, we will compare the properties of Euclidean geometry and spherical geometry.
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Voronoi cell constructions on the map
Čermák, Jan ; Hrdina, Jaroslav (referee) ; Pavlík, Jan (advisor)
This bachelor’s thesis deals with study of Voronoi cell and its representation in Voronoi diagrams and their construction on the model of Earth’s surface. At first, Voronoi diagrams and their characteristics are explained in a plane, we describe their construction using Fortune’s algorithm, then spherical geometry is explained. Then we take a look at some equations that are useful for calculating on a sphere, and we use them for calculating distances on Earth, which we approximate with a sphere. Finally we apply Fortune’s algorithm on a sphere, we explain the principles of construction of Voronoi diagrams with this algorithm on a sphere and changes compared to the planar case that must be taken care of. The goal of the thesis is to display Voronoi diagram on Google maps, thus we work with Google Maps API.
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