mirror of https://github.com/CGAL/cgal
\warning, ###Requires, i.e., whitespace
This commit is contained in:
Andreas Fabri
parent
37cb57b6bc
commit
115c25c207
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@ -106,7 +106,8 @@ double upper = 1.0);
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returns a random `IntType` from the interval
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\f$ [\mbox{lower,upper}]\f$. `IntType` can be an integral type
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as `int`, `std::ptrdiff_t`, `std::size_t`,etc. <B>Warning: In contrast to `get_int` this function may return `upper`. </B>
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as `int`, `std::ptrdiff_t`, `std::size_t`,etc.
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\warning In contrast to `get_int` this function may return `upper`.
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*/
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template <typename IntType> IntType uniform_smallint( IntType lower=0, IntType upper=9);
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@ -114,7 +115,8 @@ template <typename IntType> IntType uniform_smallint( IntType lower=0, IntType u
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returns a random `IntType` from the interval
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\f$ [\mbox{lower,upper}]\f$. `IntType` can be an integral type
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as `int`, `std::ptrdiff_t`, `std::size_t`,etc. <B>Warning: In contrast to `get_int` this function may return `upper`. </B>
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as `int`, `std::ptrdiff_t`, `std::size_t`,etc.
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\warning In contrast to `get_int` this function may return `upper`.
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*/
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template <typename IntType> IntType uniform_int( IntType lower=0, IntType upper=9);
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@ -11,25 +11,21 @@ are needed from `rnd` for each point.
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The function `perturb_points_2` perturbs each point in a given range of points by
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a random amount.
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Requirements
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--------------
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###Requires ###
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- `Creator` must be a function object accepting two
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`double` values \f$ x\f$ and \f$ y\f$ and returning an initialized point
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`(x,y)` of type `P`.
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Predefined implementations for these creators like the default are
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described in Section \ref sectionCreatorFunctionObjects.
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<UL>
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<LI>`Creator` must be a function object accepting two
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`double` values \f$ x\f$ and \f$ y\f$ and returning an initialized point
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`(x,y)` of type `P`.
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- The `value_type` of the `ForwardIterator` must be assignable
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to `P`.
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- `P` is equal to the `value_type` of the
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`ForwardIterator` when using the default initializer.
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- The expressions `to_double((*first).x())` and
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`to_double((*first).y())` must result in the respective
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coordinate values.
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Predefined implementations for these creators like the default are
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described in Section \ref sectionCreatorFunctionObjects .
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<LI>The `value_type` of the `ForwardIterator` must be assignable
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to `P`.
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<LI>`P` is equal to the `value_type` of the
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`ForwardIterator` when using the default initializer.
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<LI>The expressions `to_double((*first).x())` and
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`to_double((*first).y())` must result in the respective
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coordinate values.
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</UL>
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\sa `CGAL::points_on_segment_2`
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\sa `CGAL::points_on_square_grid_2`
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@ -51,7 +47,7 @@ namespace CGAL {
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\ingroup PkgGenerators
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creates \f$ n\f$ points equally spaced on the segment from \f$ p\f$ to \f$ q\f$,
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i.e. \f$ \forall i: 0 \le i < n: o[i] := \frac{n-i-1}{n-1}\, p +
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i.e.\ \f$ \forall i: 0 \le i < n: o[i] := \frac{n-i-1}{n-1}\, p +
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\frac{i}{n-1}\, q\f$. Returns the value of \f$ o\f$ after inserting
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the \f$ n\f$ points.
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@ -81,20 +77,19 @@ the \f$ n\f$ points.
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The function `points_on_square_grid_2` generates a given number of points on a square
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grid whose size is determined by the number of points to be generated.
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Requirements
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--------------
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<UL>
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<LI>`Creator` must be a function object accepting two
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`double` values \f$ x\f$ and \f$ y\f$ and returning an initialized point
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`(x,y)` of type `P`. Predefined implementations for these
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creators like the default can be found in
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Section \ref sectionCreatorFunctionObjects .
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<LI>The `OutputIterator` must accept values of type `P`. If the
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`OutputIterator` has a `value_type` the default
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initializer of the `creator` can be used. `P` is set to
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the `value_type` in this case.
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</UL>
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###Requires###
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- `Creator` must be a function object accepting two
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`double` values \f$ x\f$ and \f$ y\f$ and returning an initialized point
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`(x,y)` of type `P`. Predefined implementations for these
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creators like the default can be found in
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Section \ref sectionCreatorFunctionObjects.
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- The `OutputIterator` must accept values of type `P`. If the
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`OutputIterator` has a `value_type` the default
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initializer of the `creator` can be used. `P` is set to
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the `value_type` in this case.
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\sa `CGAL::perturb_points_2`
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\sa `CGAL::points_on_segment_2`
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@ -123,22 +118,19 @@ in the range \f$ [first,last)\f$.
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Three random numbers are needed from `rnd` for each point.
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Returns the value of `first2` after inserting the \f$ n\f$ points.
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Requirements
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--------------
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###Requires ###
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<UL>
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<LI>`Creator` must be a function object accepting two
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`double` values \f$ x\f$ and \f$ y\f$ and returning an initialized point
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`(x,y)` of type `P`. Predefined implementations for these
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creators like the default can be found in
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Section \ref sectionCreatorFunctionObjects .
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<LI>The `value_type` of the `RandomAccessIterator` must be
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assignable to `P`. `P` is equal to the `value_type` of the
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`RandomAccessIterator` when using the default initializer.
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<LI>The expressions `to_double((*first).x())` and
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`to_double((*first).y())` must result in the respective
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coordinate values.
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</UL>
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- `Creator` must be a function object accepting two
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`double` values \f$ x\f$ and \f$ y\f$ and returning an initialized point
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`(x,y)` of type `P`. Predefined implementations for these
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creators like the default can be found in
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Section \ref sectionCreatorFunctionObjects.
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- The `value_type` of the `RandomAccessIterator` must be
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assignable to `P`. `P` is equal to the `value_type` of the
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`RandomAccessIterator` when using the default initializer.
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- The expressions `to_double((*first).x())` and
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`to_double((*first).y())` must result in the respective
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coordinate values.
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\sa `CGAL::perturb_points_2`
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\sa `CGAL::points_on_segment_2`
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@ -218,7 +210,7 @@ typedef const Point_2& reference;
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/*!
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\f$ g\f$ is an input iterator creating points of type `Point_2` uniformly
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distributed in the open disc with radius \f$ r\f$,
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i.e. \f$ |*g| < r\f$ . Two random numbers are needed from
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i.e.\ \f$ |*g| < r\f$. Two random numbers are needed from
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`rnd` for each point.
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*/
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@ -292,8 +284,8 @@ typedef const Point_2& reference;
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/*!
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\f$ g\f$ is an input iterator creating points of type `Point_2` uniformly
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distributed in the half-open square with side length \f$ 2 a\f$, centered
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at the origin, i.e. \f$ \forall p = *g: -a \le p.x() < a\f$ and
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\f$ -a \le p.y() < a\f$ .
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at the origin, i.e.\ \f$ \forall p = *g: -a \le p.x() < a\f$ and
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\f$ -a \le p.y() < a\f$.
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Two random numbers are needed from `rnd` for each point.
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*/
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@ -371,7 +363,7 @@ typedef const Point_2& reference;
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/*!
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\f$ g\f$ is an input iterator creating points of type `Point_2` uniformly
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distributed on the circle with radius \f$ r\f$,
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i.e. \f$ |*g| == r\f$ . A single random number is needed from
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i.e.\ \f$ |*g| == r\f$. A single random number is needed from
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`rnd` for each point.
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*/
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@ -445,7 +437,7 @@ typedef const Point_2& reference;
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/*!
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\f$ g\f$ is an input iterator creating points of type `Point_2` uniformly
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distributed on the segment from \f$ p\f$ to \f$ q\f$ (excluding \f$ q\f$),
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i.e. \f$ *g == (1-\lambda)\, p + \lambda q\f$ where \f$ 0 \le\lambda< 1\f$ .
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i.e.\ \f$ *g == (1-\lambda)\, p + \lambda q\f$ where \f$ 0 \le\lambda< 1\f$.
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A single random number is needed from `rnd` for each point.
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\require The expressions `to_double(p.x())` and `to_double(p.y())` must result in the respective `double` representation of the coordinates of \f$ p\f$, and similarly for \f$ q\f$.
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*/
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@ -519,9 +511,9 @@ typedef const Point_2& reference;
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/*!
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\f$ g\f$ is an input iterator creating points of type `Point_2` uniformly
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distributed on the boundary of the square with side length \f$ 2 a\f$,
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centered at the origin, i.e. \f$ \forall p = *g:\f$ one
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centered at the origin, i.e.\ \f$ \forall p = *g:\f$ one
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coordinate is either \f$ a\f$ or \f$ -a\f$ and for the
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other coordinate \f$ c\f$ holds \f$ -a \le c < a\f$ .
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other coordinate \f$ c\f$ holds \f$ -a \le c < a\f$.
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A single random number is needed from `rnd` for each point.
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*/
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@ -612,7 +604,7 @@ std::size_t n, std::size_t i = 0);
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/*!
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returns the range in which the point
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coordinates lie, i.e. \f$ \forall x: |x| \leq\f$ `range()` and
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coordinates lie, i.e.\ \f$ \forall x: |x| \leq\f$ `range()` and
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\f$ \forall y: |y| \leq\f$`range()`
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*/
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double range();
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@ -11,24 +11,21 @@ inserting the \f$ n\f$ points.
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The function `points_on_cube_grid_3` generates a given number of points on a cubic
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grid whose size is determined by the number of points to be generated.
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Requirements
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--------------
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###Requires###
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- `Creator` must be a function object accepting three
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`double` values \f$ x\f$, \f$ y\f$, and \f$ z\f$ and returning an initialized
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point `(x,y,z)` of type `P`. Predefined implementations for
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these creators like the default can be found in
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Section \ref sectionCreatorFunctionObjects .
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- The `OutputIterator` must accept values of type `P`. If the
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`OutputIterator` has a `value_type` the default
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initializer of the `creator` can be used. `P` is set to
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the `value_type` in this case.
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<UL>
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<LI>`Creator` must be a function object accepting three
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`double` values \f$ x\f$, \f$ y\f$, and \f$ z\f$ and returning an initialized
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point `(x,y,z)` of type `P`. Predefined implementations for
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these creators like the default can be found in
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Section \ref sectionCreatorFunctionObjects .
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<LI>The `OutputIterator` must accept values of type `P`. If the
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`OutputIterator` has a `value_type` the default
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initializer of the `creator` can be used. `P` is set to
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the `value_type` in this case.
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</UL>
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`CGAL::points_on_square_grid_2`
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\sa `CGAL::points_on_square_grid_2`
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`CGAL::random_selection`
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\sa `CGAL::random_selection`
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*/
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template <class OutputIterator, Creator creator>
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@ -36,7 +36,7 @@ typedef Hidden_type value_type;
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/// @{
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/*!
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return an absolute bound for
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returns an absolute bound for
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the coordinates of all generated points.
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*/
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double range() const;
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@ -31,8 +31,8 @@ on a circle (`Random_points_on_circle_2`),
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on a segment (`Random_points_on_segment`),
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and on a square (`Random_points_on_square_2`).
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For generating grid points we provide three functions,
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`points_on_segment_2()`,
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`points_on_square_grid_2()` that write to output iterators and
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`::points_on_segment_2()`,
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`::points_on_square_grid_2()` that write to output iterators and
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an input iterator `Points_on_segment_2`.
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For 3D points, input iterators are provided for random points uniformly
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@ -48,34 +48,34 @@ distributed in a \f$ d\f$-dimensional cube (`Random_points_in_cube_d`)
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or \f$ d\f$-dimensional ball (`Random_points_in_ball_d`) or on the boundary of a
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sphere (`Random_points_on_sphere_d`).
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For generating grid points, we provide the function
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`points_on_grid_d()` that writes to
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`::points_on_grid_d()` that writes to
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an output iterator.
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We also provide two functions for generating more complex geometric objects.
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The function `random_convex_set_2()` computes a random convex planar
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The function `::random_convex_set_2()` computes a random convex planar
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point set of a given size where the points are drawn from a specific
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domain and `random_polygon_2()` generates a random simple polygon from
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domain and `::random_polygon_2()` generates a random simple polygon from
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points drawn from a specific domain.
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## Random Perturbations ##
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## %Random Perturbations ##
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Degenerate input sets like grid points can be randomly perturbed by a
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small amount to produce <I>quasi</I>-degenerate test sets. This
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challenges numerical stability of algorithms using inexact arithmetic and
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exact predicates to compute the sign of expressions slightly off from zero.
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For this the function `perturb_points_2()` is provided.
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For this the function `::perturb_points_2()` is provided.
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## Adding Degeneracies ##
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For a given point set certain kinds of degeneracies can be produced
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by adding new points. The `random_selection()` function is
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by adding new points. The `::random_selection()` function is
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useful for generating multiple copies of identical points.
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The function `random_collinear_points_2()` adds collinearities to
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The function `::random_collinear_points_2()` adds collinearities to
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a point set.
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## Support Functions and Classes for Generators ##
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The function `random_selection()` chooses \f$ n\f$ items at random from a random
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The function `::random_selection()` chooses \f$ n\f$ items at random from a random
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access iterator range which is useful to produce degenerate input data
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sets with multiple entries of identical items.
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