The Region3 class represents the cartesian product of intervals Ix ✕ Iy ✕ Iz, one per axis, yielding an axis-aligned region of R^3 space. It can be thought of as an intersection of halfspaces. Regions may be open or closed in their boundaries, if any. More...

#include <gz/math/Region3.hh>

Public Member Functions
	Region3 ()=default
	Constructor.

constexpr	Region3 (Interval< T > _ix, Interval< T > _iy, Interval< T > _iz)
	Constructor.

bool	Contains (const Region3< T > &_other) const
	Check if the region contains `_other` region.

bool	Contains (const Vector3< T > &_point) const
	Check if the region contains `_point`

bool	Empty () const
	Check if the region is empty A region is empty if any of the intervals it is defined with (i.e. Ix, Iy, Iz) are.

bool	Intersects (const Region3< T > &_other) const
	Check if the region intersects `_other` region.

const Interval< T > &	Ix () const
	Get the x-axis interval for the region.

const Interval< T > &	Iy () const
	Get the y-axis interval for the region.

const Interval< T > &	Iz () const
	Get the z-axis interval for the region.

bool	operator!= (const Region3< T > &_other) const
	Inequality test operator.

bool	operator== (const Region3< T > &_other) const
	Equality test operator.

Static Public Member Functions
static constexpr Region3< T >	Closed (T _xLeft, T _yLeft, T _zLeft, T _xRight, T _yRight, T _zRight)
	Make a closed region.

static constexpr Region3< T >	Open (T _xLeft, T _yLeft, T _zLeft, T _xRight, T _yRight, T _zRight)
	Make an open region.

Static Public Attributes
static const Region3< T > &	Unbounded = detail::gUnboundedRegion3<T>
	An unbounded region (-∞, ∞) ✕ (-∞, ∞) ✕ (-∞, ∞)

Detailed Description

template<typename T>
class gz::math::Region3< T >

The Region3 class represents the cartesian product of intervals Ix ✕ Iy ✕ Iz, one per axis, yielding an axis-aligned region of R^3 space. It can be thought of as an intersection of halfspaces. Regions may be open or closed in their boundaries, if any.

Note that the Region3 class is essentially a set R ⊆ R^3. For 3D solid box semantics, use the AxisAlignedBox class instead.

Example

#include <iostream>
#include <gz/math/Region3.hh>
#include <gz/math/Vector3.hh>
 
int main(int argc, char **argv)
{
  std::cout << std::boolalpha;
 
  const gz::math::Region3d defaultRegion;
  // A default constructed region should be empty.
  std::cout << "The " << defaultRegion << " region is empty: "
            << defaultRegion.Empty() << std::endl;
 
  const gz::math::Region3d openRegion =
      gz::math::Region3d::Open(-1., -1., -1., 1., 1., 1.);
  // An open region should exclude points on its boundary.
  std::cout << "The " << openRegion << " region contains the "
            << gz::math::Vector3d::UnitX << " point: "
            << openRegion.Contains(gz::math::Vector3d::UnitX)
            << std::endl;
 
  const gz::math::Region3d closedRegion =
      gz::math::Region3d::Closed(0., 0., 0., 1., 1., 1.);
 
  // A closed region should include points on its boundary.
  std::cout << "The " << closedRegion << " region contains the "
            << gz::math::Vector3d::UnitX << " point: "
            << closedRegion.Contains(gz::math::Vector3d::UnitX)
            << std::endl;
 
  // Closed and open regions may intersect.
  std::cout << "Regions " << closedRegion << " and " << openRegion
            << " intersect: " << closedRegion.Intersects(openRegion)
            << std::endl;
 
  // The unbounded region should include all non-empty regions.
  std::cout << "The " << gz::math::Region3d::Unbounded
            << " region contains all previous non-empty intervals: "
            << (gz::math::Region3d::Unbounded.Contains(openRegion) ||
                gz::math::Region3d::Unbounded.Contains(closedRegion))
            << std::endl;
 
}

Constructor & Destructor Documentation

◆ Region3() [1/2]

template<typename T >

Region3 ( )

default

Constructor.

◆ Region3() [2/2]

template<typename T >

constexpr Region3	(	Interval< T >	_ix,
		Interval< T >	_iy,
		Interval< T >	_iz
	)

inlineconstexpr

Constructor.

Parameters

[in]	_ix	x-axis interval
[in]	_iy	y-axis interval
[in]	_iz	z-axis interval

Member Function Documentation

◆ Closed()

template<typename T >

static constexpr Region3< T > Closed	(	T	_xLeft,
		T	_yLeft,
		T	_zLeft,
		T	_xRight,
		T	_yRight,
		T	_zRight
	)

inlinestaticconstexpr

Make a closed region.

Parameters

[in]	_xLeft	leftmost x-axis interval value
[in]	_xRight	righmost x-axis interval value
[in]	_yLeft	leftmost y-axis interval value
[in]	_yRight	righmost y-axis interval value
[in]	_zLeft	leftmost z-axis interval value
[in]	_zRight	righmost z-axis interval value

Returns: the [_xLeft, _xRight] ✕ [_yLeft, _yRight] ✕ [_zLeft, _zRight] closed region

◆ Contains() [1/2]

template<typename T >

bool Contains ( const Region3< T > & _other ) const

inline

Check if the region contains _other region.

Parameters

[in] _other region to check for membership

Returns: true if it is contained, false otherwise

◆ Contains() [2/2]

template<typename T >

bool Contains ( const Vector3< T > & _point ) const

inline

Check if the region contains _point

Parameters

[in] _point point to check for membership

Returns: true if it is contained, false otherwise

Referenced by Region3< T >::operator!=(), and Region3< T >::operator==().

◆ Empty()

template<typename T >

bool Empty ( ) const

inline

Check if the region is empty A region is empty if any of the intervals it is defined with (i.e. Ix, Iy, Iz) are.

Returns: true if it is empty, false otherwise

◆ Intersects()

template<typename T >

bool Intersects ( const Region3< T > & _other ) const

inline

Check if the region intersects _other region.

Parameters

[in] _other region to check for intersection

Returns: true if it is contained, false otherwise

◆ Ix()

template<typename T >

const Interval< T > & Ix ( ) const

inline

Get the x-axis interval for the region.

Returns: the x-axis interval

◆ Iy()

template<typename T >

const Interval< T > & Iy ( ) const

inline

Get the y-axis interval for the region.

Returns: the y-axis interval

◆ Iz()

template<typename T >

const Interval< T > & Iz ( ) const

inline

Get the z-axis interval for the region.

Returns: the z-axis interval

◆ Open()

template<typename T >

static constexpr Region3< T > Open	(	T	_xLeft,
		T	_yLeft,
		T	_zLeft,
		T	_xRight,
		T	_yRight,
		T	_zRight
	)

inlinestaticconstexpr

Make an open region.

Parameters

[in]	_xLeft	leftmost x-axis interval value
[in]	_xRight	righmost x-axis interval value
[in]	_yLeft	leftmost y-axis interval value
[in]	_yRight	righmost y-axis interval value
[in]	_zLeft	leftmost z-axis interval value
[in]	_zRight	righmost z-axis interval value

Returns: the (_xLeft, _xRight) ✕ (_yLeft, _yRight) ✕ (_zLeft, _zRight) open region

◆ operator!=()

template<typename T >

bool operator!= ( const Region3< T > & _other ) const

inline

Inequality test operator.

Parameters

_other region to check for inequality

Returns: true if regions are unequal, false otherwise

References Region3< T >::Contains().

◆ operator==()

template<typename T >

bool operator== ( const Region3< T > & _other ) const

inline

Equality test operator.

Parameters

_other region to check for equality

Returns: true if regions are equal, false otherwise

References Region3< T >::Contains().

Member Data Documentation

◆ Unbounded

template<typename T >

const Region3< T > & Unbounded = detail::gUnboundedRegion3<T>

static

An unbounded region (-∞, ∞) ✕ (-∞, ∞) ✕ (-∞, ∞)

The documentation for this class was generated from the following file:

Region3.hh

Gazebo Math

API Reference

Public Member Functions

Static Public Member Functions

Static Public Attributes

Detailed Description

Example

Constructor & Destructor Documentation

◆ Region3() [1/2]

◆ Region3() [2/2]

Member Function Documentation

◆ Closed()

◆ Contains() [1/2]

◆ Contains() [2/2]

◆ Empty()

◆ Intersects()

◆ Ix()

◆ Iy()

◆ Iz()

◆ Open()

◆ operator!=()

◆ operator==()

Member Data Documentation

◆ Unbounded