mirror of https://github.com/CGAL/cgal
Last checkin before release 2.
This commit is contained in:
Lutz Kettner
parent
29ee98b567
commit
0a270d86ca
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@ -1,7 +1,7 @@
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% +------------------------------------------------------------------------+
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% | CGAL Reference Manual: generators.tex
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% +------------------------------------------------------------------------+
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% | Random sources and geometric object generators.
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% | Geometric object generators.
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% |
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% | 09.06.1997 Lutz Kettner
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% |
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@ -13,35 +13,27 @@
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\aftercprogskip\medskipamount
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\ccParDims
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\chapter{Random Sources and Geometric Object Generators}
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\chapter{Geometric Object Generators}
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\label{chapterGenerators}
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\ccChapterRelease{\generatorsRev. \ \generatorsDate}\\
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\ccChapterAuthor{Michael Hoffmann}\\
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\ccChapterAuthor{Lutz Kettner}\\
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\ccChapterAuthor{Sven Sch\"onherr}
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\ccChapterAuthor{Lutz Kettner}
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A variety of generators for random numbers and geometric objects is
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provided in \cgal. They are useful as synthetic test data sets,
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e.g.~for testing algorithms on degenerate object sets and for
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performance analysis.
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A variety of generators for geometric objects is provided in \cgal.
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They are useful as synthetic test data sets, e.g.~for testing
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algorithms on degenerate object sets and for performance analysis.
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The first section describes the random number source used for random
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generators. The second section provides useful generic functions
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related to random numbers like \ccc{CGAL_random_selection()}. The
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third section documents generators for two-dimensional point sets, the
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fourth section for three-dimensional point sets. The fifth section
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presents examples using functions from
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Section~\ref{sectionGenericFunctions} to generate composed objects
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like segments.
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%% The sixth section describes random convex sets.
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Note that the \stl\ algorithm \ccc{random_shuffle} is
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useful in this context to achieve random permutations for otherwise
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regular generators (e.g.~points on a grid or segment).
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% +------------------------------------------------------------------------+
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\input{Random}
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The first section provides useful generic functions related to random
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numbers like \ccc{CGAL_random_selection()}. The second section
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documents generators for two-dimensional point sets, the third section
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for three-dimensional point sets. The fourth section presents examples
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using functions from Section~\ref{sectionGenericFunctions} to generate
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composed objects, such as segments. The fifth section describes
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random convex sets. Note that the \stl\ algorithm
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\ccc{random_shuffle} is useful in this context to achieve random
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permutations for otherwise regular generators (e.g.~points on a grid
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or segment).
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% +------------------------------------------------------------------------+
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%\newpage
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@ -62,7 +54,7 @@ sets with multiple entries of identical items.
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class OutputIterator, class Random>
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OutputIterator CGAL_random_selection( RandomAccessIterator first,
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RandomAccessIterator last,
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Size n, OutputIterator result, Random& rnd = CGAL_random);}
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Size n, OutputIterator result, Random& rnd = default_random);}
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{ chooses a random item from the range $[\ccc{first},\ccc{last})$ and
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writes it to \ccc{result}, each item from the range with equal
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probability, and repeats this $n$ times, thus writing $n$ items to
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@ -77,6 +69,7 @@ sets with multiple entries of identical items.
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% +------------------------------------------------------------------------+
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\newpage
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\section{2D Point Generators}
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\label{sectionPointGenerators}
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Two kind of point generators are provided: First, random point
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generators and second deterministic point generators. Most random
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@ -124,13 +117,14 @@ includes local type declarations including \ccc{value_type} which
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denotes \ccc{P} here.
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\ccCreation
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\ccTwo{}{\hspace*{11cm}}
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%% \ccTwo{}{\hspace*{10cm}}
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\ccHtmlNoClassFile
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\begin{ccClassTemplate}{CGAL_Random_points_in_disc_2<P,Creator>}
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\ccCreationVariable{g}
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\ccConstructor{CGAL_Random_points_in_disc_2( double r, CGAL_Random& rnd =
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CGAL_random);}{%
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default_random);}{%
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$g$ is an input iterator creating points of type \ccc{P} uniformly
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distributed in the open disc with radius $r$,
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i.e.~$|\ccc{*g}| < r$~. Two random numbers are needed from
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@ -142,7 +136,7 @@ denotes \ccc{P} here.
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\begin{ccClassTemplate}{CGAL_Random_points_on_circle_2<P,Creator>}
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\ccCreationVariable{g}
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\ccConstructor{CGAL_Random_points_on_circle_2( double r, CGAL_Random& rnd =
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CGAL_random);}{%
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default_random);}{%
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$g$ is an input iterator creating points of type \ccc{P} uniformly
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distributed on the circle with radius $r$,
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i.e.~$|\ccc{*g}| == r$~. A single random number is needed from
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@ -154,7 +148,7 @@ denotes \ccc{P} here.
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\begin{ccClassTemplate}{CGAL_Random_points_in_square_2<P,Creator>}
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\ccCreationVariable{g}
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\ccConstructor{CGAL_Random_points_in_square_2( double a, CGAL_Random& rnd =
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CGAL_random);}{%
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default_random);}{%
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$g$ is an input iterator creating points of type \ccc{P} uniformly
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distributed in the half-open square with side length $2 a$, centered
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at the origin, i.e.~$\forall p = \ccc{*g}: -a \le p.x() < a$ and
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@ -167,7 +161,7 @@ denotes \ccc{P} here.
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\begin{ccClassTemplate}{CGAL_Random_points_on_square_2<P,Creator>}
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\ccCreationVariable{g}
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\ccConstructor{CGAL_Random_points_on_square_2( double a, CGAL_Random& rnd =
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CGAL_random);}{%
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default_random);}{%
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$g$ is an input iterator creating points of type \ccc{P} uniformly
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distributed on the boundary of the square with side length $2 a$,
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centered at the origin, i.e.~$\forall p = \ccc{*g}:$ one
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@ -181,7 +175,7 @@ denotes \ccc{P} here.
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\begin{ccClassTemplate}{CGAL_Random_points_on_segment_2<P,Creator>}
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\ccCreationVariable{g}
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\ccConstructor{CGAL_Random_points_on_segment_2( const P& p, const P& q,
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CGAL_Random& rnd = CGAL_random);}{%
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CGAL_Random& rnd = default_random);}{%
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$g$ is an input iterator creating points of type \ccc{P} uniformly
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distributed on the segment from $p$ to $q$ (excluding $q$),
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i.e.~$\ccc{*g} == (1-\lambda)\, p + \lambda q$ where $0 \le \lambda < 1$~.
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@ -278,7 +272,7 @@ exact predicates to compute the sign of expressions slightly off from zero.
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\ccFunction{template <class ForwardIterator>
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void CGAL_perturb_points_2( ForwardIterator first, ForwardIterator last,
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double xeps, double yeps = xeps, CGAL_Random& rnd = CGAL_random,
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double xeps, double yeps = xeps, CGAL_Random& rnd = default_random,
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Creator creator = CGAL_Creator_uniform_2<double,P>);}
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{ perturbs the points in the range $[\ccc{first},\ccc{last})$ by
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replacing each point with a random point from the rectangle
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@ -311,7 +305,7 @@ a point set.
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\ccFunction{template <class RandomAccessIterator, class OutputIterator>
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OutputIterator CGAL_random_collinear_points_2( RandomAccessIterator first,
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RandomAccessIterator last,
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size_t n, OutputIterator first2, CGAL_Random& rnd = CGAL_random,
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size_t n, OutputIterator first2, CGAL_Random& rnd = default_random,
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Creator creator = CGAL_Creator_uniform_2<double,P>);}
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{ randomly chooses two points from the range $[\ccc{first},\ccc{last})$,
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creates a random third point on the segment connecting this two
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@ -383,6 +377,7 @@ Figure~\ref{figurePointGenerator}}{Figure <A HREF="#PointGenerators">
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</TD></TR></TABLE>
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\end{ccHtmlOnly}
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\newpage
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The second example demonstrates the point generators with integer
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points. Arithmetic with \ccc{double}'s is sufficient to produce
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@ -455,13 +450,13 @@ includes local type declarations including \ccc{value_type} which
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denotes \ccc{P} here.
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\ccCreation
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\ccTwo{}{\hspace*{11cm}}
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\ccHtmlNoClassFile
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\begin{ccClassTemplate}{CGAL_Random_points_in_sphere_3<P,Creator>}
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\ccCreationVariable{g}
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\ccConstructor{CGAL_Random_points_in_sphere_3( double r, CGAL_Random& rnd =
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CGAL_random);}{%
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default_random);}{%
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$g$ is an input iterator creating points of type \ccc{P} uniformly
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distributed in the open sphere with radius $r$,
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i.e.~$|\ccc{*g}| < r$~.
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@ -472,7 +467,7 @@ denotes \ccc{P} here.
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\begin{ccClassTemplate}{CGAL_Random_points_on_sphere_3<P,Creator>}
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\ccCreationVariable{g}
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\ccConstructor{CGAL_Random_points_on_sphere_3( double r, CGAL_Random& rnd =
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CGAL_random);}{%
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default_random);}{%
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$g$ is an input iterator creating points of type \ccc{P} uniformly
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distributed on the boundary of a sphere with radius $r$,
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i.e.~$|\ccc{*g}| == r$~. Two random numbers are needed from
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@ -484,7 +479,7 @@ denotes \ccc{P} here.
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\begin{ccClassTemplate}{CGAL_Random_points_in_cube_3<P,Creator>}
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\ccCreationVariable{g}
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\ccConstructor{CGAL_Random_points_in_cube_3( double a, CGAL_Random& rnd =
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CGAL_random);}{%
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default_random);}{%
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$g$ is an input iterator creating points of type \ccc{P} uniformly
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distributed in the half-open cube with side length $2 a$, centered
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at the origin, i.e.~$\forall p = \ccc{*g}: -a \le p.x(),p.y(),p.z() < a$~.
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|
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@ -1,7 +1,7 @@
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% +------------------------------------------------------------------------+
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% | CGAL Reference Manual: generators.tex
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% +------------------------------------------------------------------------+
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% | Random sources and geometric object generators.
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% | Geometric object generators.
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% |
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% | 09.06.1997 Lutz Kettner
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% |
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@ -13,35 +13,27 @@
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\aftercprogskip\medskipamount
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\ccParDims
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\chapter{Random Sources and Geometric Object Generators}
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\chapter{Geometric Object Generators}
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\label{chapterGenerators}
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\ccChapterRelease{\generatorsRev. \ \generatorsDate}\\
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\ccChapterAuthor{Michael Hoffmann}\\
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\ccChapterAuthor{Lutz Kettner}\\
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\ccChapterAuthor{Sven Sch\"onherr}
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\ccChapterAuthor{Lutz Kettner}
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|
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|
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A variety of generators for random numbers and geometric objects is
|
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provided in \cgal. They are useful as synthetic test data sets,
|
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e.g.~for testing algorithms on degenerate object sets and for
|
||||
performance analysis.
|
||||
A variety of generators for geometric objects is provided in \cgal.
|
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They are useful as synthetic test data sets, e.g.~for testing
|
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algorithms on degenerate object sets and for performance analysis.
|
||||
|
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The first section describes the random number source used for random
|
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generators. The second section provides useful generic functions
|
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related to random numbers like \ccc{CGAL_random_selection()}. The
|
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third section documents generators for two-dimensional point sets, the
|
||||
fourth section for three-dimensional point sets. The fifth section
|
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presents examples using functions from
|
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Section~\ref{sectionGenericFunctions} to generate composed objects
|
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like segments.
|
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%% The sixth section describes random convex sets.
|
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Note that the \stl\ algorithm \ccc{random_shuffle} is
|
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useful in this context to achieve random permutations for otherwise
|
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regular generators (e.g.~points on a grid or segment).
|
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% +------------------------------------------------------------------------+
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\input{Random}
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The first section provides useful generic functions related to random
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numbers like \ccc{CGAL_random_selection()}. The second section
|
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documents generators for two-dimensional point sets, the third section
|
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for three-dimensional point sets. The fourth section presents examples
|
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using functions from Section~\ref{sectionGenericFunctions} to generate
|
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composed objects, such as segments. The fifth section describes
|
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random convex sets. Note that the \stl\ algorithm
|
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\ccc{random_shuffle} is useful in this context to achieve random
|
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permutations for otherwise regular generators (e.g.~points on a grid
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or segment).
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% +------------------------------------------------------------------------+
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%\newpage
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@ -62,7 +54,7 @@ sets with multiple entries of identical items.
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class OutputIterator, class Random>
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OutputIterator CGAL_random_selection( RandomAccessIterator first,
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RandomAccessIterator last,
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Size n, OutputIterator result, Random& rnd = CGAL_random);}
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Size n, OutputIterator result, Random& rnd = default_random);}
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{ chooses a random item from the range $[\ccc{first},\ccc{last})$ and
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writes it to \ccc{result}, each item from the range with equal
|
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probability, and repeats this $n$ times, thus writing $n$ items to
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@ -77,6 +69,7 @@ sets with multiple entries of identical items.
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% +------------------------------------------------------------------------+
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\newpage
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\section{2D Point Generators}
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\label{sectionPointGenerators}
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Two kind of point generators are provided: First, random point
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generators and second deterministic point generators. Most random
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|
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@ -124,13 +117,14 @@ includes local type declarations including \ccc{value_type} which
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denotes \ccc{P} here.
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\ccCreation
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\ccTwo{}{\hspace*{11cm}}
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%% \ccTwo{}{\hspace*{10cm}}
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\ccHtmlNoClassFile
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\begin{ccClassTemplate}{CGAL_Random_points_in_disc_2<P,Creator>}
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\ccCreationVariable{g}
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\ccConstructor{CGAL_Random_points_in_disc_2( double r, CGAL_Random& rnd =
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CGAL_random);}{%
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default_random);}{%
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$g$ is an input iterator creating points of type \ccc{P} uniformly
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distributed in the open disc with radius $r$,
|
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i.e.~$|\ccc{*g}| < r$~. Two random numbers are needed from
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@ -142,7 +136,7 @@ denotes \ccc{P} here.
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\begin{ccClassTemplate}{CGAL_Random_points_on_circle_2<P,Creator>}
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\ccCreationVariable{g}
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\ccConstructor{CGAL_Random_points_on_circle_2( double r, CGAL_Random& rnd =
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CGAL_random);}{%
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default_random);}{%
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$g$ is an input iterator creating points of type \ccc{P} uniformly
|
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distributed on the circle with radius $r$,
|
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i.e.~$|\ccc{*g}| == r$~. A single random number is needed from
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@ -154,7 +148,7 @@ denotes \ccc{P} here.
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\begin{ccClassTemplate}{CGAL_Random_points_in_square_2<P,Creator>}
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\ccCreationVariable{g}
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\ccConstructor{CGAL_Random_points_in_square_2( double a, CGAL_Random& rnd =
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CGAL_random);}{%
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default_random);}{%
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$g$ is an input iterator creating points of type \ccc{P} uniformly
|
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distributed in the half-open square with side length $2 a$, centered
|
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at the origin, i.e.~$\forall p = \ccc{*g}: -a \le p.x() < a$ and
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|
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@ -167,7 +161,7 @@ denotes \ccc{P} here.
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\begin{ccClassTemplate}{CGAL_Random_points_on_square_2<P,Creator>}
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\ccCreationVariable{g}
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\ccConstructor{CGAL_Random_points_on_square_2( double a, CGAL_Random& rnd =
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CGAL_random);}{%
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default_random);}{%
|
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$g$ is an input iterator creating points of type \ccc{P} uniformly
|
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distributed on the boundary of the square with side length $2 a$,
|
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centered at the origin, i.e.~$\forall p = \ccc{*g}:$ one
|
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|
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@ -181,7 +175,7 @@ denotes \ccc{P} here.
|
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\begin{ccClassTemplate}{CGAL_Random_points_on_segment_2<P,Creator>}
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\ccCreationVariable{g}
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\ccConstructor{CGAL_Random_points_on_segment_2( const P& p, const P& q,
|
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CGAL_Random& rnd = CGAL_random);}{%
|
||||
CGAL_Random& rnd = default_random);}{%
|
||||
$g$ is an input iterator creating points of type \ccc{P} uniformly
|
||||
distributed on the segment from $p$ to $q$ (excluding $q$),
|
||||
i.e.~$\ccc{*g} == (1-\lambda)\, p + \lambda q$ where $0 \le \lambda < 1$~.
|
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|
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@ -278,7 +272,7 @@ exact predicates to compute the sign of expressions slightly off from zero.
|
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|
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\ccFunction{template <class ForwardIterator>
|
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void CGAL_perturb_points_2( ForwardIterator first, ForwardIterator last,
|
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double xeps, double yeps = xeps, CGAL_Random& rnd = CGAL_random,
|
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double xeps, double yeps = xeps, CGAL_Random& rnd = default_random,
|
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Creator creator = CGAL_Creator_uniform_2<double,P>);}
|
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{ perturbs the points in the range $[\ccc{first},\ccc{last})$ by
|
||||
replacing each point with a random point from the rectangle
|
||||
|
|
@ -311,7 +305,7 @@ a point set.
|
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\ccFunction{template <class RandomAccessIterator, class OutputIterator>
|
||||
OutputIterator CGAL_random_collinear_points_2( RandomAccessIterator first,
|
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RandomAccessIterator last,
|
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size_t n, OutputIterator first2, CGAL_Random& rnd = CGAL_random,
|
||||
size_t n, OutputIterator first2, CGAL_Random& rnd = default_random,
|
||||
Creator creator = CGAL_Creator_uniform_2<double,P>);}
|
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{ randomly chooses two points from the range $[\ccc{first},\ccc{last})$,
|
||||
creates a random third point on the segment connecting this two
|
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@ -383,6 +377,7 @@ Figure~\ref{figurePointGenerator}}{Figure <A HREF="#PointGenerators">
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</TD></TR></TABLE>
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\end{ccHtmlOnly}
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||||
\newpage
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|
||||
The second example demonstrates the point generators with integer
|
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points. Arithmetic with \ccc{double}'s is sufficient to produce
|
||||
|
|
@ -455,13 +450,13 @@ includes local type declarations including \ccc{value_type} which
|
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denotes \ccc{P} here.
|
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|
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\ccCreation
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\ccTwo{}{\hspace*{11cm}}
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|
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\ccHtmlNoClassFile
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\begin{ccClassTemplate}{CGAL_Random_points_in_sphere_3<P,Creator>}
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\ccCreationVariable{g}
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\ccConstructor{CGAL_Random_points_in_sphere_3( double r, CGAL_Random& rnd =
|
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CGAL_random);}{%
|
||||
default_random);}{%
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||||
$g$ is an input iterator creating points of type \ccc{P} uniformly
|
||||
distributed in the open sphere with radius $r$,
|
||||
i.e.~$|\ccc{*g}| < r$~.
|
||||
|
|
@ -472,7 +467,7 @@ denotes \ccc{P} here.
|
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\begin{ccClassTemplate}{CGAL_Random_points_on_sphere_3<P,Creator>}
|
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\ccCreationVariable{g}
|
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\ccConstructor{CGAL_Random_points_on_sphere_3( double r, CGAL_Random& rnd =
|
||||
CGAL_random);}{%
|
||||
default_random);}{%
|
||||
$g$ is an input iterator creating points of type \ccc{P} uniformly
|
||||
distributed on the boundary of a sphere with radius $r$,
|
||||
i.e.~$|\ccc{*g}| == r$~. Two random numbers are needed from
|
||||
|
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@ -484,7 +479,7 @@ denotes \ccc{P} here.
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\begin{ccClassTemplate}{CGAL_Random_points_in_cube_3<P,Creator>}
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\ccCreationVariable{g}
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\ccConstructor{CGAL_Random_points_in_cube_3( double a, CGAL_Random& rnd =
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CGAL_random);}{%
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default_random);}{%
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$g$ is an input iterator creating points of type \ccc{P} uniformly
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distributed in the half-open cube with side length $2 a$, centered
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at the origin, i.e.~$\forall p = \ccc{*g}: -a \le p.x(),p.y(),p.z() < a$~.
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Reference in New Issue