CGAL 6.2 - Geometric Object Generators: CGAL::Random_points_in_tetrahedron_3< Point_3, Creator > Class Template Reference

CGAL 6.2 - Geometric Object Generators

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CGAL::Random_points_in_tetrahedron_3< Point_3, Creator > Class Template Reference

`#include <CGAL/point_generators_3.h>`

## Definition

template<typename Point_3, typename Creator>
class CGAL::Random_points_in_tetrahedron_3< Point_3, Creator >

The class `Random_points_in_tetrahedron_3` is an input iterator creating points uniformly distributed inside a tetrahedron.

The default `Creator` is `Creator_uniform_3<Kernel_traits<Point_3>::Kernel::RT,Point_3>`.

Is model of
  `InputIterator`
  `PointGenerator`

See also
  `CGAL::Random_points_on_segment_3<Point_3, Creator>`
  `CGAL::Random_points_in_cube_3<Point_3, Creator>`
  `CGAL::Random_points_in_triangle_3<Point_3, Creator>`
  `CGAL::Random_points_on_sphere_3<Point_3, Creator>`

Examples
  Generator/random_points_tetrahedron_and_triangle_3.cpp.

## Types
typedef std::input_iterator_tag | iterator_category
typedef Point_3 | value_type
typedef std::ptrdiff_t | difference_type
typedef const Point_3 * | pointer
typedef const Point_3 & | reference

## Function
| Random_points_in_tetrahedron_3 (Point_3 &p, Point_3 &q, Point_3 &r, Point_3 &s, Random &rnd=get_default_random())
| creates an input iterator `g` generating points of type `Point_3` uniformly distributed inside the tetrahedron with vertices \( p, q, r \) and \( s \), i.e., \(*g = \alpha p + \beta q + \gamma r + \delta s \), for some \( \alpha, \beta, \gamma, \delta \in [0, 1] \) and \( \alpha + \beta + \gamma + \delta = 1 \).
| Random_points_in_tetrahedron_3 (Tetrahedron_3 &t, Random &rnd=get_default_random())
| creates an input iterator `g` generating points of type `Point_3` uniformly distributed inside a tetrahedron \(t\) with vertices \( p, q, r \) and \( s \), i.e., \(*g = \alpha p + \beta q + \gamma r + \delta s \), for some \( \alpha, \beta, \gamma, \delta \in [0, 1] \) and \( \alpha + \beta + \gamma + \delta = 1 \).

## Constructor & Destructor Documentation

## ◆ Random_points_in_tetrahedron_3() [1/2]

template<typename Point_3 , typename Creator >

CGAL::Random_points_in_tetrahedron_3< Point_3, Creator >::Random_points_in_tetrahedron_3 | ( | Point_3 & | p,
|  | Point_3 & | q,
|  | Point_3 & | r,
|  | Point_3 & | s,
|  | Random & | rnd = `get_default_random()`
| ) |  |

creates an input iterator `g` generating points of type `Point_3` uniformly distributed inside the tetrahedron with vertices \( p, q, r \) and \( s \), i.e., \(*g = \alpha p + \beta q + \gamma r + \delta s \), for some \( \alpha, \beta, \gamma, \delta \in [0, 1] \) and \( \alpha + \beta + \gamma + \delta = 1 \).

Three random numbers are needed from `rnd` for each point.

## ◆ Random_points_in_tetrahedron_3() [2/2]

template<typename Point_3 , typename Creator >

CGAL::Random_points_in_tetrahedron_3< Point_3, Creator >::Random_points_in_tetrahedron_3 | ( | Tetrahedron_3 & | t,
|  | Random & | rnd = `get_default_random()`
| ) |  |

creates an input iterator `g` generating points of type `Point_3` uniformly distributed inside a tetrahedron \(t\) with vertices \( p, q, r \) and \( s \), i.e., \(*g = \alpha p + \beta q + \gamma r + \delta s \), for some \( \alpha, \beta, \gamma, \delta \in [0, 1] \) and \( \alpha + \beta + \gamma + \delta = 1 \).

Three random numbers are needed from `rnd` for each point.