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I work as a researcher in the Algorithms group of the Institute of Operating Systems and Computer Networks
of the Technische Universität Braunschweig, Germany. Together with prof. Sandor Fekete, I work in the field of computational geometry.
Computational geometry is a discipline of computer science that developed as a subarea of algorithms research in the early nineteen-seventies. It was motivated by application areas such as computer graphics and vision. Computational geometers aim to develop efficient algorithms and data structures for solving geometric problems. Examples are: "Where is the nearest letter box?", or "Will my new tv-set fit in the trunk of my car? What if I leave the box behind?", or "What is the fastest way to my daughter's school so I can pick her up in time?". These physical objects (boxes, shortest paths) are
represented as simple, geometric objects, like points, lines, and polygons (e.g., a city map) or balls, blocks, and other shapes (e.g., boxes, tv-sets, etc.) in a mathematical problem formulation. The emphasis lies on solving discrete mathematical problems involving mainly such simple objects, hence it is possible to focus on the combinatorial properties of the problem.
However, there are other applications that involve geometric computations. For example, a database storing the inventory (location and amount of goods) of a hardware factory can be imagined as a database with points in four-dimensional space, where each point represents one goods (say, hammers). The coordinates of the point indicate, for example, the exact location of the box with hammers (corridor number, shelf number, box number) as well as the amount of hammers on stock. Hence, geometric computations are used in various fields: engineering, visualization, robotics, motion planning, virtual reality, computer graphics and computer vision, operations research, pattern recognition, crystallography, computational biology, cartography, and many more.
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