Represents a tetrahedral geometric shape defined by four points. More...

#include </home/docs/checkouts/readthedocs.org/user_builds/axom/checkouts/v0.7.0/src/axom/primal/geometry/Tetrahedron.hpp>

Public Types
using	PointType = Point< T, NDIMS >

using	VectorType = Vector< T, NDIMS >

using	SphereType = Sphere< T, NDIMS >

Public Member Functions
AXOM_HOST_DEVICE	Tetrahedron ()
	Default constructor. Creates a degenerate tetrahedron. More...

AXOM_HOST_DEVICE	Tetrahedron (const PointType &A, const PointType &B, const PointType &C, const PointType &D)
	Tetrahedron constructor from 4 points A,B,C,D. 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 bool	degenerate (double eps=1.0e-12) const
	Returns whether the tetrahedron is degenerate. More...

Point< double, 4 >	physToBarycentric (const PointType &p, bool skipNormalization=false) const
	Returns the barycentric coordinates of a point within a tetrahedron. More...

PointType	baryToPhysical (const Point< double, 4 > &bary) const
	Returns the physical coordinates of a barycentric point. More...

std::ostream &	print (std::ostream &os) const
	Simple formatted print of a tetrahedron instance. More...

AXOM_HOST_DEVICE double	signedVolume () const
	Returns the signed volume of the tetrahedron. More...

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

template<int TDIM = NDIMS>
std::enable_if< TDIM==3, SphereType >::type	circumsphere () const
	Returns the circumsphere (circumscribing sphere) of the tetrahedron. More...

Static Public Attributes
static constexpr int	NUM_TET_VERTS = 4

Detailed Description

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

Represents a tetrahedral geometric shape defined by four points.

Template Parameters

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

Member Typedef Documentation

◆ PointType

template<typename T, int NDIMS>

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

◆ VectorType

template<typename T, int NDIMS>

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

◆ SphereType

template<typename T, int NDIMS>

using axom::primal::Tetrahedron< T, NDIMS >::SphereType = Sphere<T, NDIMS>

Constructor & Destructor Documentation

◆ Tetrahedron() [1/2]

template<typename T, int NDIMS>

AXOM_HOST_DEVICE axom::primal::Tetrahedron< T, NDIMS >::Tetrahedron ( )

inline

Default constructor. Creates a degenerate tetrahedron.

References AXOM_HOST_DEVICE.

◆ Tetrahedron() [2/2]

template<typename T, int NDIMS>

AXOM_HOST_DEVICE axom::primal::Tetrahedron< T, NDIMS >::Tetrahedron	(	const PointType &	A,
		const PointType &	B,
		const PointType &	C,
		const PointType &	D
	)

inline

Tetrahedron constructor from 4 points A,B,C,D.

Parameters

[in]	A	Vertex A of the tetrahedron
[in]	B	Vertex B of the tetrahedron
[in]	C	Vertex C of the tetrahedron
[in]	D	Vertex D of the tetrahedron

Note: The orientation of the tetrahedron is determined from the scalar triple product of the vectors from B, C and D to A, respectively, i.e. \( dot(B-A, cross(C-A, D-A)) \).

Member Function Documentation

◆ operator[]() [1/2]

template<typename T, int NDIMS>

AXOM_HOST_DEVICE PointType& axom::primal::Tetrahedron< 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, or 3

References SLIC_ASSERT.

◆ operator[]() [2/2]

template<typename T, int NDIMS>

AXOM_HOST_DEVICE const PointType& axom::primal::Tetrahedron< 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, or 3

References AXOM_HOST_DEVICE, and SLIC_ASSERT.

◆ degenerate()

template<typename T, int NDIMS>

AXOM_HOST_DEVICE bool axom::primal::Tetrahedron< T, NDIMS >::degenerate ( double eps = 1.0e-12 ) const

inline

Returns whether the tetrahedron is degenerate.

Returns: true iff the tetrahedron is degenerate (has near zero volume)

References axom::utilities::isNearlyEqual().

◆ physToBarycentric()

template<typename T, int NDIMS>

Point<double, 4> axom::primal::Tetrahedron< T, NDIMS >::physToBarycentric	(	const PointType &	p,
		bool	skipNormalization = `false`
	)		const

inline

Returns the barycentric coordinates of a point within a tetrahedron.

Parameters

[in]	p	The point at which we want to compute barycentric coordinates
[in]	skipNormalization	Determines if the result should be normalized by the volume of the tetrahedron. One might want to skip this if they were only interested in the relative weights rather than their actual amounts

Postcondition: The barycentric coordinates sum to 1 when skipNormalization is false Otherwise, the sum of coordinates will be proportional to volume of the tetrahedron (Specifically, they should sum to the parallelpiped volume, which is 6x the volume).

References axom::primal::abs(), axom::primal::Point< T, NDIMS >::array(), axom::primal::Vector< T, NDIMS >::scalar_triple_product(), and axom::primal::NumericArray< T, SIZE >::sum().

◆ baryToPhysical()

template<typename T, int NDIMS>

PointType axom::primal::Tetrahedron< T, NDIMS >::baryToPhysical ( const Point< double, 4 > & bary ) const

inline

Returns the physical coordinates of a barycentric point.

Parameters

[in] bary Barycentric coordinates relative to this tetrahedron

References axom::primal::Point< T, NDIMS >::array(), axom::utilities::isNearlyEqual(), axom::primal::Tetrahedron< T, NDIMS >::NUM_TET_VERTS, and SLIC_CHECK_MSG.

◆ print()

template<typename T, int NDIMS>

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

inline

Simple formatted print of a tetrahedron instance.

Parameters

os	The output stream to write to

Returns: A reference to the modified ostream

References AXOM_HOST_DEVICE.

◆ signedVolume()

template<typename T, int NDIMS>

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

inline

Returns the signed volume of the tetrahedron.

See also: volume()

References AXOM_HOST_DEVICE.

◆ volume()

template<typename T, int NDIMS>

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

inline

Returns the absolute (unsigned) volume of the tetrahedron.

See also: signedVolume()

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

◆ circumsphere()

template<typename T, int NDIMS>

template<int TDIM = NDIMS>

std::enable_if<TDIM == 3, SphereType>::type axom::primal::Tetrahedron< T, NDIMS >::circumsphere ( ) const

inline

Returns the circumsphere (circumscribing sphere) of the tetrahedron.

Derived from formula on https://mathworld.wolfram.com/Circumsphere.html but uses observation that radius can be derived from distance to a vertex

Note: This function is only available for 3D tetrahedra in 3D

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

Member Data Documentation

◆ NUM_TET_VERTS

template<typename T, int NDIMS>

constexpr int axom::primal::Tetrahedron< T, NDIMS >::NUM_TET_VERTS = 4

static

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

/home/docs/checkouts/readthedocs.org/user_builds/axom/checkouts/v0.7.0/src/axom/primal/geometry/Tetrahedron.hpp

Public Types

Public Member Functions

Static Public Attributes

Detailed Description

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

Member Typedef Documentation

◆ PointType

◆ VectorType

◆ SphereType

Constructor & Destructor Documentation

◆ Tetrahedron() [1/2]

◆ Tetrahedron() [2/2]

Member Function Documentation

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ degenerate()

◆ physToBarycentric()

◆ baryToPhysical()

◆ print()

◆ signedVolume()

◆ volume()

◆ circumsphere()

Member Data Documentation

◆ NUM_TET_VERTS

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