Computational Geometry: Fundamental Structures

Authored by: Mark de Berg , Bettina Speckmann

Handbook of Data Structures and Applications

Print publication date:  March  2018
Online publication date:  February  2018

Print ISBN: 9781498701853
eBook ISBN: 9781315119335
Adobe ISBN:

10.1201/9781315119335-65

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Abstract

Computational geometry deals with the design and analysis of algorithms and data structures for problems involving spatial data. The questions that are studied range from basic problems such as line-segment intersection (“Compute all intersection points in a given set of line segments in the plane.”) to quite involved problems such as motion-planning (“Compute a collision-free path for a robot in workspace from a given start position to a given goal position.”) Because spatial data plays an important role in many areas within and outside of computer science—CAD/CAM, computer graphics and virtual reality, and geography are just a few examples—computational geometry has a broad range of applications. Computational geometry emerged from the general algorithms area in the late 1970s. It experienced a rapid growth in the 1980s and by now is a recognized discipline with its own conferences and journals and many researchers working in the area. It is a beautiful field with connections to other areas of algorithms research, to application areas like the ones mentioned earlier, and to areas of mathematics such as combinatorial geometry.

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