# Algorithmic Geometry

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{{Short description|1995 mathematics text}}
{{about|the book|the field|computational geometry}}
{{Infobox book
| author            = [Jean-Daniel Boissonnat](/source/Jean-Daniel_Boissonnat) and [Mariette Yvinec](/source/Mariette_Yvinec)
| pub_date          = 1995
| language          = French
| title_orig        = Géometrie algorithmique
| publisher         = Edusciences
| translator        = Hervé Brönnimann
| image             = File:Algorithmic_Geometry.jpg
}}
{{italic title}}
'''''Algorithmic Geometry''''' is a textbook on [computational geometry](/source/computational_geometry). It was originally written in the [French language](/source/French_language) by [Jean-Daniel Boissonnat](/source/Jean-Daniel_Boissonnat) and [Mariette Yvinec](/source/Mariette_Yvinec), and published as ''Géometrie algorithmique'' by Edusciences in 1995. It was translated into English by Hervé Brönnimann, with improvements to some proofs and additional exercises, and published by the [Cambridge University Press](/source/Cambridge_University_Press) in 1998.{{r|zbl|lms|mr}}

==Topics==
The book covers the theoretical background and analysis of [algorithm](/source/algorithm)s in computational geometry, their implementation details, and their applications.{{r|zbl}} It is grouped into five sections, the first of which covers background material on the design and analysis of algorithms and [data structure](/source/data_structure)s, including [computational complexity theory](/source/computational_complexity_theory), and techniques for designing [randomized algorithm](/source/randomized_algorithm)s. Its subsequent sections each consist of a chapter on the mathematics of a subtopic in this area, presented at the level of detail needed to analyze the algorithms, followed by two or three chapters on algorithms for that subtopic.{{r|lms}}

The topics presented in these sections and chapters include [convex hull](/source/convex_hull)s and [convex hull algorithms](/source/convex_hull_algorithms), low-dimensional randomized [linear programming](/source/linear_programming), [point set triangulation](/source/point_set_triangulation) for two- and three-dimensional data, [arrangements of hyperplanes](/source/arrangement_of_hyperplanes), of line segments, and of triangles, [Voronoi diagram](/source/Voronoi_diagram)s, and [Delaunay triangulation](/source/Delaunay_triangulation)s.{{r|lms|mr}}

==Audience and reception==
The book can be used as a graduate textbook, or as a reference for computational geometry research.{{r|zbl}} Reviewer [Peter McMullen](/source/Peter_McMullen) calls it "a welcome addition to the shelves of anyone interested in algorithmic geometry".{{r|lms}}

==References==
<references>

<ref name=zbl>{{citation|title=none|first=S.|last=Stifter|journal=[zbMATH](/source/zbMATH)|zbl=0917.68212}}</ref>

<ref name=mr>{{citation|title=none|last=Hecker|first=Hans-Dietrich|journal=[Mathematical Reviews](/source/Mathematical_Reviews)|year=1999|mr=1631175}}</ref>

<ref name=lms>{{citation|last=McMullen|first=Peter|authorlink=Peter McMullen|date=November 1999|doi=10.1112/blms/31.6.758|issue=6|journal=[Bulletin of the London Mathematical Society](/source/Bulletin_of_the_London_Mathematical_Society)|pages=758–759|title=none|volume=31}}</ref>

</references>

{{Authority control}}

Category:Computational geometry
Category:Mathematics textbooks
Category:1995 non-fiction books
Category:1998 non-fiction books

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