Construction of Geometric Models for Moving Points

Written by Tomáš Vomáčka

Tomáš Vomáčka

University of West Bohemia

Seminar in Czech
May 31, 2010 at 13:30
University of West Bohemia, UL411

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Abstract

Geometric models for moving points represent a valuable tool of modern computational geometry. In this work, we focus mainly on kinetic Delaunay triangulation which is a special case of the ordinary (static) Delaunay triangulation intended to be used together with moving points without losing its abilities. The first part of the following text describes the overall properties of Delaunay triangulation and the algorithms which are most commonly used for its construction. The following part describes the process of kinetization of the static data structure (together with the properties of the kinetic model). In the next part, we show some of the applications of kinetic Delaunay triangulation, such as collision detection, simulation of crowds, mathematical simulations in the field of fluid dynamics and motion interpolation. Finally, we present our own method for kinetic Delaunay triangulation management together with some new theoretical findings and two applications -- kinetic Delaunay triangulation used as a tool for video representation and as a core part of an early warning system for air traffic control.