Voronoi Diagrams and Delaunay Triangulations

Voronoi Diagrams and Delaunay Triangulations

Franz Aurenhammer, Rolf Klein, Der-Tsai Lee


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Voronoi diagrams partition space according to the influence certain sites exert on their environment. Since the 17th century, such structures play an important role in many areas like Astronomy, Physics, Chemistry, Biology, Ecology, Economics, Mathematics and Computer Science. They help to describe zones of political influence, to determine the hospital nearest to an accident site, to compute collision-free paths for mobile robots, to reconstruct curves and surfaces from sample points, to refine triangular meshes, and to design location strategies for competing markets.

This unique book offers a state-of-the-art view of Voronoi diagrams and their structure, and it provides efficient algorithms towards their computation.

Readers with an entry-level background in algorithms can enjoy a guided tour of gently increasing difficulty through a fascinating area. Lecturers might find this volume a welcome source for their courses on computational geometry. Experts are offered a broader view, including many alternative solutions, and up-to-date references to the existing literature; they might benefit in their own research or application development.

  • Introduction
  • Elementary Properties
  • Basic Algorithms
  • Advanced Properties
  • Generalized Sites
  • Higher Dimensions
  • General Spaces & Distances
  • Applications and Relatives
  • Miscellanea
  • Alternative Solutions in Rd
  • Conclusions

Readership: Students of mathematics and computer science, scientists and engineers working in mathematics, natural sciences and economics.