Defines an oriented Sphere in 2-D (i.e., a circle) or 3-D given by its center, \( \mathcal{X} \) and radius \( \mathcal{R} \). The Sphere object provides associated operations on a sphere, such as, signed distance and orientation. More...

#include </home/docs/checkouts/readthedocs.org/user_builds/axom/checkouts/develop/src/axom/primal/geometry/Sphere.hpp>

Inheritance diagram for axom::primal::Sphere< T, NDIMS >:

[legend]

Public Types
using	PointType = primal::Point< T, NDIMS >

Public Member Functions
AXOM_HOST_DEVICE T	getRadius () const
	Returns the radius of the Sphere. More...

AXOM_HOST_DEVICE const PointType &	getCenter () const
	Returns the center of the Sphere. More...

AXOM_HOST_DEVICE T	getVolume () const
	Returns the n-dimensional volume enclosed by the Sphere. More...

AXOM_HOST_DEVICE T	computeSignedDistance (const PointType &q) const
	Computes the signed distance of a point to the Sphere's boundary. More...

AXOM_HOST_DEVICE int	getOrientation (const PointType &q, double TOL=1.e-9) const
	Computes the orientation of a point with respect to the Sphere. More...

AXOM_HOST_DEVICE bool	contains (const PointType &q, bool includeBoundary=true) const
	Tests if a point lies inside this sphere. More...

AXOM_HOST_DEVICE bool	intersectsWith (const Sphere< T, NDIMS > &sphere, double TOL=1.e-9) const
	Tests if this sphere instance intersects with another sphere. More...

AXOM_HOST_DEVICE bool	contains (const Sphere< T, NDIMS > &other, double margin=0.0) const
	Tests if this sphere completely contains another sphere. More...

std::ostream &	print (std::ostream &os) const
	Prints the Sphere information in the given output stream. More...

Constructors
AXOM_HOST_DEVICE	Sphere (T radius=1.0)
	Constructs a Sphere centered at origin with the given radius. More...

AXOM_HOST_DEVICE	Sphere (const PointType &center, T radius=1.0)
	Constructs a Sphere with the given center and radius. More...

AXOM_HOST_DEVICE	Sphere (const T *center, T radius=1.0)
	Constructs a Sphere with the given center and radius. More...

Detailed Description

template<typename T, int NDIMS>
class axom::primal::Sphere< T, NDIMS >

Defines an oriented Sphere in 2-D (i.e., a circle) or 3-D given by its center, \( \mathcal{X} \) and radius \( \mathcal{R} \). The Sphere object provides associated operations on a sphere, such as, signed distance and orientation.

Template Parameters

T	the coordinate type, e.g., double, float, etc.
NDIMS	the number of dimensions

Member Typedef Documentation

◆ PointType

template<typename T , int NDIMS>

using axom::primal::Sphere< T, NDIMS >::PointType = primal::Point<T, NDIMS>

Constructor & Destructor Documentation

◆ Sphere() [1/3]

template<typename T , int NDIMS>

AXOM_HOST_DEVICE axom::primal::Sphere< T, NDIMS >::Sphere ( T radius = 1.0 )

inlineexplicit

Constructs a Sphere centered at origin with the given radius.

Parameters

[in] radius the radius of the Sphere (optional).

Note: If a radius is not supplied, the default radius is 1.0.

◆ Sphere() [2/3]

template<typename T , int NDIMS>

AXOM_HOST_DEVICE axom::primal::Sphere< T, NDIMS >::Sphere	(	const PointType &	center,
		T	radius = `1.0`
	)

inlineexplicit

Constructs a Sphere with the given center and radius.

Parameters

[in]	center	user-supplied center.
[in]	radius	the radius of the Sphere (optional).

Note: If a radius is not supplied, the default radius is 1.0.

◆ Sphere() [3/3]

template<typename T , int NDIMS>

AXOM_HOST_DEVICE axom::primal::Sphere< T, NDIMS >::Sphere	(	const T *	center,
		T	radius = `1.0`
	)

explicit

Constructs a Sphere with the given center and radius.

Parameters

[in]	center	user-supplied center.
[in]	radius	the radius of the Sphere (optional).

Note: If a radius is not supplied, the default radius is 1.0.

Precondition: center != nullptr

References SLIC_ASSERT.

Member Function Documentation

◆ getRadius()

template<typename T , int NDIMS>

AXOM_HOST_DEVICE T axom::primal::Sphere< T, NDIMS >::getRadius ( ) const

inline

Returns the radius of the Sphere.

Returns: r the radius of the Sphere.

◆ getCenter()

template<typename T , int NDIMS>

AXOM_HOST_DEVICE const PointType& axom::primal::Sphere< T, NDIMS >::getCenter ( ) const

inline

Returns the center of the Sphere.

Returns: c pointer to array that holds the center of the Sphere.

Note: c points to an array that is NDIMS long.

Postcondition: c != nullptr

◆ getVolume()

template<typename T , int NDIMS>

AXOM_HOST_DEVICE T axom::primal::Sphere< T, NDIMS >::getVolume ( ) const

inline

Returns the n-dimensional volume enclosed by the Sphere.

◆ computeSignedDistance()

template<typename T , int NDIMS>

AXOM_HOST_DEVICE T axom::primal::Sphere< T, NDIMS >::computeSignedDistance ( const PointType & q ) const

inline

Computes the signed distance of a point to the Sphere's boundary.

Parameters

[in] q The test point

Returns: d the computed signed distance of the point q to the sphere.

Note

The signed distance of a point q is:

negative inside the sphere
positive outside the sphere
zero on the boundary

References axom::primal::Vector< T, NDIMS >::norm().

◆ getOrientation()

template<typename T , int NDIMS>

AXOM_HOST_DEVICE int axom::primal::Sphere< T, NDIMS >::getOrientation	(	const PointType &	q,
		double	TOL = `1.e-9`
	)		const

inline

Computes the orientation of a point with respect to the Sphere.

Parameters

[in]	q	The test point
[in]	TOL	user-supplied tolerance. Optional. Default is 1.e-9.

Returns: orient the orientation of q with respect to the sphere.

Note

This method returns one of the following values:

ON_BOUNDARY : if q is on the sphere's boundary
ON_POSITIVE_SIDE : if q is outside the sphere
ON_NEGATIVE_SIDE : if q is inside the sphere

See also: OrientationResult for the list of possible return values.

References axom::primal::Sphere< T, NDIMS >::computeSignedDistance(), axom::utilities::isNearlyEqual(), axom::primal::ON_BOUNDARY, axom::primal::ON_NEGATIVE_SIDE, and axom::primal::ON_POSITIVE_SIDE.

◆ contains() [1/2]

template<typename T , int NDIMS>

AXOM_HOST_DEVICE bool axom::primal::Sphere< T, NDIMS >::contains	(	const PointType &	q,
		bool	includeBoundary = `true`
	)		const

inline

Tests if a point lies inside this sphere.

Parameters

[in]	q	The test point
[in]	includeBoundary	should points on the boundary count as contained? (default true)

Returns: true if q lies inside (and possibly on) the sphere, false otherwise.

Note: This is an exact-arithmetic-free containment test. When a tolerance-aware answer is required (for example, to treat points within EPS of the surface as lying on the boundary), use getOrientation(), which returns primal::ON_BOUNDARY within the supplied tolerance, or compare the result of computeSignedDistance() against your own scale-aware tolerance.

◆ intersectsWith()

template<typename T , int NDIMS>

AXOM_HOST_DEVICE bool axom::primal::Sphere< T, NDIMS >::intersectsWith	(	const Sphere< T, NDIMS > &	sphere,
		double	TOL = `1.e-9`
	)		const

inline

Tests if this sphere instance intersects with another sphere.

Parameters

[in]	sphere	the sphere object to check for intersection
[in]	TOL	tolerance for intersection test. Optional. If not specified the default tolerance is set to 1.e-9.

Returns: status true if the sphere intersects, false otherwise.

References axom::primal::Sphere< T, NDIMS >::getCenter(), axom::primal::Sphere< T, NDIMS >::getRadius(), axom::utilities::isNearlyEqual(), and axom::primal::Vector< T, NDIMS >::squared_norm().

◆ contains() [2/2]

template<typename T , int NDIMS>

AXOM_HOST_DEVICE bool axom::primal::Sphere< T, NDIMS >::contains	(	const Sphere< T, NDIMS > &	other,
		double	margin = `0.0`
	)		const

inline

Tests if this sphere completely contains another sphere.

Parameters

[in]	other	The sphere object to check for containment
[in]	margin	Amount to add to other's radius before comparing.

Note: a sphere does contain itself.

Returns: true if this sphere contains the other, false otherwise.

References axom::primal::Sphere< T, NDIMS >::getCenter(), axom::primal::Sphere< T, NDIMS >::getRadius(), and axom::primal::Vector< T, NDIMS >::norm().

◆ print()

template<typename T , int NDIMS>

std::ostream & axom::primal::Sphere< T, NDIMS >::print ( std::ostream & os ) const

Prints the Sphere information in the given output stream.

Parameters

[in,out] os the output stream to write to.

Note: This method is primarily used for debugging.

Returns: s the modified output stream object.

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

/home/docs/checkouts/readthedocs.org/user_builds/axom/checkouts/develop/src/axom/primal/geometry/Sphere.hpp

Public Types

Public Member Functions

Detailed Description

template<typename T, int NDIMS> class axom::primal::Sphere< T, NDIMS >

Member Typedef Documentation

◆ PointType

Constructor & Destructor Documentation

◆ Sphere() [1/3]

◆ Sphere() [2/3]

◆ Sphere() [3/3]

Member Function Documentation

◆ getRadius()

◆ getCenter()

◆ getVolume()

◆ computeSignedDistance()

◆ getOrientation()

◆ contains() [1/2]

◆ intersectsWith()

◆ contains() [2/2]

◆ print()

template<typename T, int NDIMS>
class axom::primal::Sphere< T, NDIMS >