mirror of https://github.com/CGAL/cgal
43 lines
1.6 KiB
TeX
43 lines
1.6 KiB
TeX
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% | Reference manual page: Convex_hull_d_ref/intro.tex
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% +------------------------------------------------------------------------+
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%\clearpage
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%\section{Reference Pages for dD Convex Hulls and Delaunay Triangulations}
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\ccRefChapter{dD Convex Hulls and Delaunay Triangulations}
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\label{chap:convex_hull_d_ref}
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\ccChapterAuthor{Susan Hert \and Michael Seel}
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A subset $S \subseteq \R^3$ is convex if for any two points $p$ and $q$
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in the set the line segment with endpoints $p$ and $q$ is contained
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in $S$. The convex hull\ccIndexMainItemDef{convex hull} of a set $S$ is
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the smallest convex set containing
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$S$. The convex hull of a set of points $P$ is a convex
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polytope with vertices in $P$. A point in $P$ is an extreme point
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(with respect to $P$)\ccIndexMainItemDef{extreme point} if it is a vertex
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of the convex hull of $P$.
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\cgal\ provides functions for computing convex hulls in two, three
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and arbitrary dimensions as well as functions for testing if a given set of
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points in is strongly convex or not. This chapter describes the class
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available for arbitrary dimensions and its companion class for
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computing the nearest and furthest side Delaunay triangulation.
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\section{Classified Reference Pages}
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\ccHeading{Concepts}
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\ccRefConceptPage{ConvexHullTraits_d} \\
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\ccRefConceptPage{DelaunayLiftedTraits_d} \\
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\ccRefConceptPage{DelaunayTraits_d} \\
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\ccHeading{Classes}
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\ccRefIdfierPage{CGAL::Convex_hull_d_traits_3<R>} \\
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\ccRefIdfierPage{CGAL::Convex_hull_d<R>} \\
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\ccRefIdfierPage{CGAL::Delaunay_d< R, Lifted_R >}
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\clearpage
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