Represents an hexahedral geometric shape defined by eight points. More...

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

Public Types
enum	{ NUM_HEX_VERTS = 8 , NUM_TRIANGULATE = 24 }

using	PointType = Point< T, NDIMS >

using	VectorType = Vector< T, NDIMS >

using	TetrahedronType = Tetrahedron< T, NDIMS >

using	NumArrayType = NumericArray< T, NDIMS >

Public Member Functions
	Hexahedron ()=default
	Default constructor. Creates a degenerate hexahedron. More...

AXOM_HOST_DEVICE	Hexahedron (const PointType &p, const PointType &q, const PointType &r, const PointType &s, const PointType &t, const PointType &u, const PointType &v, const PointType &w)
	Creates an hexahedron from the 8 points p,q,r,s,t,u,v,w. More...

AXOM_HOST_DEVICE	Hexahedron (const PointType *pts)
	Hexahedron constructor from an array of Points. More...

AXOM_HOST_DEVICE	Hexahedron (const axom::ArrayView< PointType > pts)
	Hexahedron constructor from an Array of Points. More...

AXOM_HOST_DEVICE	Hexahedron (std::initializer_list< PointType > pts)
	Hexahedron constructor from an initializer list of Points. More...

AXOM_HOST_DEVICE PointType &	operator[] (int idx)
	Index operator to get the i^th vertex. More...

AXOM_HOST_DEVICE const PointType &	operator[] (int idx) const
	Index operator to get the i^th vertex. More...

AXOM_HOST_DEVICE PointType	vertexMean () const
	Computes the average of the hexahedron's vertex positions. More...

AXOM_HOST_DEVICE double	signedVolume () const
	Finds the signed volume of the hexahedron. More...

AXOM_HOST_DEVICE double	volume () const
	Returns the absolute (unsigned) volume of the hexahedron. More...

AXOM_HOST_DEVICE void	triangulate (axom::StackArray< TetrahedronType, NUM_TRIANGULATE > &tets)
	Method to decompose a Hexahedron into 24 Tetrahedrons. Each Tetrahedron consists of 4 points: (1) The mean of all Hexahedron points (2,3) Two adjacent vertices on a Hexahedron face (4) The mean of the current Hexahedron face. More...

AXOM_HOST_DEVICE bool	equals (const Hexahedron &other, double eps=1.e-24) const
	Test if this Hexahedron is equal to another, within a tolerance. More...

std::ostream &	print (std::ostream &os) const
	Simple formatted print of an hexahedron instance. More...

Detailed Description

template<typename T, int NDIMS = 3>
class axom::primal::Hexahedron< T, NDIMS >

Represents an hexahedral geometric shape defined by eight points.

Template Parameters

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

There are eight vertices in the hexahedron, labelled P through W as the constructor's arguments. They are accessible using the square-brackets operator, with P being index 0, Q index 1, through W as index 7.

Here's a diagram showing a cube with the labeled vertices.

*
* S +---------+ R              +y
*   |\        |\
*   |  \      |  \              ^
*   | W + --------+ V           |
* P +---|-----+ Q |             |
*   \   |     \   |             -----> +x
*    \  |      \  |              \
*     \ |       \ |               \
*   T  +----------+ U              >
*                                   +z
*

Member Typedef Documentation

◆ PointType

template<typename T , int NDIMS = 3>

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

◆ VectorType

template<typename T , int NDIMS = 3>

using axom::primal::Hexahedron< T, NDIMS >::VectorType = Vector<T, NDIMS>

◆ TetrahedronType

template<typename T , int NDIMS = 3>

using axom::primal::Hexahedron< T, NDIMS >::TetrahedronType = Tetrahedron<T, NDIMS>

◆ NumArrayType

template<typename T , int NDIMS = 3>

using axom::primal::Hexahedron< T, NDIMS >::NumArrayType = NumericArray<T, NDIMS>

Member Enumeration Documentation

◆ anonymous enum

template<typename T , int NDIMS = 3>

anonymous enum

Enumerator
NUM_HEX_VERTS
NUM_TRIANGULATE

Constructor & Destructor Documentation

◆ Hexahedron() [1/5]

template<typename T , int NDIMS = 3>

axom::primal::Hexahedron< T, NDIMS >::Hexahedron ( )

default

Default constructor. Creates a degenerate hexahedron.

◆ Hexahedron() [2/5]

template<typename T , int NDIMS = 3>

AXOM_HOST_DEVICE axom::primal::Hexahedron< T, NDIMS >::Hexahedron	(	const PointType &	p,
		const PointType &	q,
		const PointType &	r,
		const PointType &	s,
		const PointType &	t,
		const PointType &	u,
		const PointType &	v,
		const PointType &	w
	)

inline

Creates an hexahedron from the 8 points p,q,r,s,t,u,v,w.

Parameters

[in]	Point	corresponding to vertex p of the hexahedron.
[in]	Point	corresponding to vertex q of the hexahedron.
[in]	Point	corresponding to vertex r of the hexahedron.
[in]	Point	corresponding to vertex s of the hexahedron.
[in]	Point	corresponding to vertex t of the hexahedron.
[in]	Point	corresponding to vertex u of the hexahedron.
[in]	Point	corresponding to vertex v of the hexahedron.
[in]	Point	corresponding to vertex w of the hexahedron.

◆ Hexahedron() [3/5]

template<typename T , int NDIMS = 3>

AXOM_HOST_DEVICE axom::primal::Hexahedron< T, NDIMS >::Hexahedron ( const PointType * pts )

inlineexplicit

Hexahedron constructor from an array of Points.

Parameters

[in] pts An array containing at least 8 Points.

Note: It is the responsiblity of the caller to pass an array with at least 8 Points

References axom::primal::Hexahedron< T, NDIMS >::NUM_HEX_VERTS.

◆ Hexahedron() [4/5]

template<typename T , int NDIMS = 3>

AXOM_HOST_DEVICE axom::primal::Hexahedron< T, NDIMS >::Hexahedron ( const axom::ArrayView< PointType > pts )

inlineexplicit

Hexahedron constructor from an Array of Points.

Parameters

[in] pts An ArrayView containing 8 Points.

References axom::primal::Hexahedron< T, NDIMS >::NUM_HEX_VERTS, axom::ArrayView< T, DIM, SPACE >::size(), and SLIC_ASSERT.

◆ Hexahedron() [5/5]

template<typename T , int NDIMS = 3>

AXOM_HOST_DEVICE axom::primal::Hexahedron< T, NDIMS >::Hexahedron ( std::initializer_list< PointType > pts )

inlineexplicit

Hexahedron constructor from an initializer list of Points.

Parameters

[in] pts an initializer list containing 8 Points

References axom::primal::Hexahedron< T, NDIMS >::NUM_HEX_VERTS, and SLIC_ASSERT.

Member Function Documentation

◆ operator[]() [1/2]

template<typename T , int NDIMS = 3>

AXOM_HOST_DEVICE PointType& axom::primal::Hexahedron< T, NDIMS >::operator[] ( int idx )

inline

Index operator to get the i^th vertex.

Parameters

idx	The index of the desired vertex

Precondition: idx is 0, 1, 2, 3, 4, 5, 6, or 7

References axom::primal::Hexahedron< T, NDIMS >::NUM_HEX_VERTS, and SLIC_ASSERT.

◆ operator[]() [2/2]

template<typename T , int NDIMS = 3>

AXOM_HOST_DEVICE const PointType& axom::primal::Hexahedron< T, NDIMS >::operator[] ( int idx ) const

inline

Index operator to get the i^th vertex.

Parameters

idx	The index of the desired vertex

Precondition: idx is 0, 1, 2, 3, 4, 5, 6, or 7

References axom::primal::Hexahedron< T, NDIMS >::NUM_HEX_VERTS, and SLIC_ASSERT.

◆ vertexMean()

template<typename T , int NDIMS = 3>

AXOM_HOST_DEVICE PointType axom::primal::Hexahedron< T, NDIMS >::vertexMean ( ) const

inline

Computes the average of the hexahedron's vertex positions.

Returns: A point at the mean of the hexahedron's vertices

References axom::primal::Point< T, NDIMS >::array(), and axom::primal::Hexahedron< T, NDIMS >::NUM_HEX_VERTS.

◆ signedVolume()

template<typename T , int NDIMS = 3>

AXOM_HOST_DEVICE double axom::primal::Hexahedron< T, NDIMS >::signedVolume ( ) const

inline

Finds the signed volume of the hexahedron.

Uses algorithm in Grandy, J. Efficient computation of volume of hexahedral cells. United States: N. p., 1997. Web. doi:10.2172/632793.

Returns: The volume of the hexahedron

Note: Indices are different from the original paper

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

◆ volume()

template<typename T , int NDIMS = 3>

AXOM_HOST_DEVICE double axom::primal::Hexahedron< T, NDIMS >::volume ( ) const

inline

Returns the absolute (unsigned) volume of the hexahedron.

See also: signedVolume()

References axom::utilities::abs(), and axom::primal::Hexahedron< T, NDIMS >::signedVolume().

◆ triangulate()

template<typename T , int NDIMS = 3>

AXOM_HOST_DEVICE void axom::primal::Hexahedron< T, NDIMS >::triangulate ( axom::StackArray< TetrahedronType, NUM_TRIANGULATE > & tets )

inline

Method to decompose a Hexahedron into 24 Tetrahedrons. Each Tetrahedron consists of 4 points: (1) The mean of all Hexahedron points (2,3) Two adjacent vertices on a Hexahedron face (4) The mean of the current Hexahedron face.

Parameters

tets	[out] The tetrahedrons

Note: Assumes tets is pre-allocated

References axom::primal::Point< T, NDIMS >::midpoint(), and axom::primal::Hexahedron< T, NDIMS >::vertexMean().

◆ equals()

template<typename T , int NDIMS = 3>

AXOM_HOST_DEVICE bool axom::primal::Hexahedron< T, NDIMS >::equals	(	const Hexahedron< T, NDIMS > &	other,
		double	eps = `1.e-24`
	)		const

inline

Test if this Hexahedron is equal to another, within a tolerance.

Note: This function can be an expensive operation

References axom::primal::Hexahedron< T, NDIMS >::NUM_HEX_VERTS, and axom::primal::squared_distance().

◆ print()

template<typename T , int NDIMS = 3>

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

inline

Simple formatted print of an hexahedron instance.

Parameters

os	The output stream to write to

Returns: A reference to the modified ostream

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/Hexahedron.hpp

Public Types

Public Member Functions

Detailed Description

template<typename T, int NDIMS = 3> class axom::primal::Hexahedron< T, NDIMS >

Member Typedef Documentation

◆ PointType

◆ VectorType

◆ TetrahedronType

◆ NumArrayType

Member Enumeration Documentation

◆ anonymous enum

Constructor & Destructor Documentation

◆ Hexahedron() [1/5]

◆ Hexahedron() [2/5]

◆ Hexahedron() [3/5]

◆ Hexahedron() [4/5]

◆ Hexahedron() [5/5]

Member Function Documentation

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ vertexMean()

◆ signedVolume()

◆ volume()

◆ triangulate()

◆ equals()

◆ print()

template<typename T, int NDIMS = 3>
class axom::primal::Hexahedron< T, NDIMS >