Represents a triangular geometric shape defined by three points. More...

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

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

[legend]

Public Types
using	PointType = Point< T, NDIMS >

using	VectorType = Vector< T, NDIMS >

using	SphereType = Sphere< T, NDIMS >

Public Member Functions
AXOM_HOST_DEVICE	Triangle ()
	Default constructor. Creates a degenerate triangle. More...

AXOM_HOST_DEVICE	Triangle (const PointType &A, const PointType &B, const PointType &C)
	Custom Constructor. Creates a triangle from the 3 points A,B,C. 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...

template<int TDIM = NDIMS>
AXOM_HOST_DEVICE std::enable_if< TDIM==3, VectorType >::type	normal () const
	Returns the normal of the triangle (not normalized) More...

template<int TDIM = NDIMS>
AXOM_HOST_DEVICE std::enable_if< TDIM==3, double >::type	area () const
	Returns the area of the triangle (3D specialization) More...

template<int TDIM = NDIMS>
AXOM_HOST_DEVICE std::enable_if< TDIM==2, double >::type	area () const
	Returns the area of the triangle (2D specialization) More...

template<int TDIM = NDIMS>
AXOM_HOST_DEVICE std::enable_if< TDIM==2, double >::type	signedArea () const
	Returns the signed area of a 2D triangle. More...

AXOM_HOST_DEVICE double	volume () const
	Returns the volume of the triangle (synonym for area()) More...

template<int TDIM = NDIMS>
AXOM_HOST_DEVICE std::enable_if< TDIM==2, double >::type	signedVolume () const
	Returns the signed volume of a 2D triangle. More...

template<int TDIM = NDIMS>
std::enable_if< TDIM==2, SphereType >::type	circumsphere () const
	Returns the circumsphere (circumscribing circle) of the triangle. More...

Point< double, 3 >	physToBarycentric (const PointType &p, bool skipNormalization=false) const
	Returns the barycentric coordinates of a point within a triangle. More...

PointType	baryToPhysical (const Point< double, 3 > &bary) const
	Returns the physical coordinates of a barycentric point. More...

AXOM_HOST_DEVICE bool	degenerate (double eps=1.0e-12) const
	Returns whether the triangle is degenerate. More...

bool	checkInTriangle (const PointType &p, double eps=1e-8) const
	Returns whether Point P is in the triangle for some 3d Triangle. More...

AXOM_HOST_DEVICE double	angle (int idx) const
	Computes the request angle corresponding to the given vertex ID. More...

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

Static Public Attributes
static constexpr int	DIM = NDIMS

static constexpr int	NUM_TRI_VERTS = 3

Detailed Description

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

Represents a triangular geometric shape defined by three points.

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::Triangle< T, NDIMS >::PointType = Point<T, NDIMS>

◆ VectorType

template<typename T , int NDIMS>

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

◆ SphereType

template<typename T , int NDIMS>

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

Constructor & Destructor Documentation

◆ Triangle() [1/2]

template<typename T , int NDIMS>

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

inline

Default constructor. Creates a degenerate triangle.

◆ Triangle() [2/2]

template<typename T , int NDIMS>

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

inline

Custom Constructor. Creates a triangle from the 3 points A,B,C.

Parameters

[in]	A	point instance corresponding to vertex A of the triangle.
[in]	B	point instance corresponding to vertex B of the triangle.
[in]	C	point instance corresponding to vertex C of the triangle.

Member Function Documentation

◆ operator[]() [1/2]

template<typename T , int NDIMS>

AXOM_HOST_DEVICE PointType& axom::primal::Triangle< 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 or 2

References axom::primal::Triangle< T, NDIMS >::NUM_TRI_VERTS, and SLIC_ASSERT.

◆ operator[]() [2/2]

template<typename T , int NDIMS>

AXOM_HOST_DEVICE const PointType& axom::primal::Triangle< 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 or 2

References axom::primal::Triangle< T, NDIMS >::NUM_TRI_VERTS, and SLIC_ASSERT.

◆ normal()

template<typename T , int NDIMS>

template<int TDIM = NDIMS>

AXOM_HOST_DEVICE std::enable_if<TDIM == 3, VectorType>::type axom::primal::Triangle< T, NDIMS >::normal ( ) const

inline

Returns the normal of the triangle (not normalized)

Precondition: This function is only valid when NDIMS = 3

Returns: n triangle normal when NDIMS=3, zero vector otherwise

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

◆ area() [1/2]

template<typename T , int NDIMS>

template<int TDIM = NDIMS>

AXOM_HOST_DEVICE std::enable_if<TDIM == 3, double>::type axom::primal::Triangle< T, NDIMS >::area ( ) const

inline

Returns the area of the triangle (3D specialization)

References axom::primal::Triangle< T, NDIMS >::normal().

◆ area() [2/2]

template<typename T , int NDIMS>

template<int TDIM = NDIMS>

AXOM_HOST_DEVICE std::enable_if<TDIM == 2, double>::type axom::primal::Triangle< T, NDIMS >::area ( ) const

inline

Returns the area of the triangle (2D specialization)

References axom::utilities::abs(), and axom::primal::Triangle< T, NDIMS >::signedArea().

◆ signedArea()

template<typename T , int NDIMS>

template<int TDIM = NDIMS>

AXOM_HOST_DEVICE std::enable_if<TDIM == 2, double>::type axom::primal::Triangle< T, NDIMS >::signedArea ( ) const

inline

Returns the signed area of a 2D triangle.

The area is positive when the vertices are oriented counter-clockwise.

Note: This function is only available for triangles in 2D since signed areas don't make sense for 3D triangles

References axom::numerics::determinant().

◆ volume()

template<typename T , int NDIMS>

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

inline

Returns the volume of the triangle (synonym for area())

See also: area()

References axom::primal::Triangle< T, NDIMS >::area().

◆ signedVolume()

template<typename T , int NDIMS>

template<int TDIM = NDIMS>

AXOM_HOST_DEVICE std::enable_if<TDIM == 2, double>::type axom::primal::Triangle< T, NDIMS >::signedVolume ( ) const

inline

Returns the signed volume of a 2D triangle.

References axom::primal::Triangle< T, NDIMS >::signedArea().

◆ circumsphere()

template<typename T , int NDIMS>

template<int TDIM = NDIMS>

std::enable_if<TDIM == 2, SphereType>::type axom::primal::Triangle< T, NDIMS >::circumsphere ( ) const

inline

Returns the circumsphere (circumscribing circle) of the triangle.

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

Note: This function is only available for triangles in 2D

References axom::numerics::determinant().

◆ physToBarycentric()

template<typename T , int NDIMS>

Point<double, 3> axom::primal::Triangle< T, NDIMS >::physToBarycentric	(	const PointType &	p,
		bool	skipNormalization = `false`
	)		const

inline

Returns the barycentric coordinates of a point within a triangle.

Parameters

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

Precondition: The point lies in this triangle's plane.

Postcondition: The barycentric coordinates sum to 1 when skipNormalization is false Otherwise, the sum of coordinates will be proportional to area of the triangle

Algorithm adapted from Real Time Collision Detection by Christer Ericson.

References axom::primal::abs(), axom::primal::Triangle< T, NDIMS >::area(), axom::primal::Vector< T, NDIMS >::cross_product(), axom::primal::Triangle< T, NDIMS >::DIM, axom::utilities::isNearlyEqual(), and SLIC_CHECK.

◆ baryToPhysical()

template<typename T , int NDIMS>

PointType axom::primal::Triangle< T, NDIMS >::baryToPhysical ( const Point< double, 3 > & bary ) const

inline

Returns the physical coordinates of a barycentric point.

Parameters

[in] bary Barycentric coordinates relative to this triangle

Returns: Physical point represented by bary

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

◆ degenerate()

template<typename T , int NDIMS>

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

inline

Returns whether the triangle is degenerate.

Returns: true iff the triangle is degenerate (0 area)

See also: primal::Point

References axom::primal::Triangle< T, NDIMS >::area(), and axom::utilities::isNearlyEqual().

◆ checkInTriangle()

template<typename T , int NDIMS>

bool axom::primal::Triangle< T, NDIMS >::checkInTriangle	(	const PointType &	p,
		double	eps = `1e-8`
	)		const

inline

Returns whether Point P is in the triangle for some 3d Triangle.

Returns: true iff P is in the triangle

See also: primal::Point

References axom::utilities::isNearlyEqual(), and axom::primal::Triangle< T, NDIMS >::physToBarycentric().

◆ angle()

template<typename T , int NDIMS>

AXOM_HOST_DEVICE double axom::primal::Triangle< T, NDIMS >::angle ( int idx ) const

inline

Computes the request angle corresponding to the given vertex ID.

Parameters

[in] idx the index of the corresponding vertex

Returns: alpha the incidence angle in the range [0, pi].

Precondition: idx >= 0 && idx < NUM_TRI_VERTS

References axom::utilities::clampVal(), axom::numerics::dot_product(), and SLIC_ASSERT.

◆ print()

template<typename T , int NDIMS>

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

inline

Simple formatted print of a triangle instance.

Parameters

os	The output stream to write to

Returns: A reference to the modified ostream

Member Data Documentation

◆ DIM

template<typename T , int NDIMS>

constexpr int axom::primal::Triangle< T, NDIMS >::DIM = NDIMS

staticconstexpr

◆ NUM_TRI_VERTS

template<typename T , int NDIMS>

constexpr int axom::primal::Triangle< T, NDIMS >::NUM_TRI_VERTS = 3

staticconstexpr

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

/home/docs/checkouts/readthedocs.org/user_builds/axom/checkouts/latest/src/axom/primal/geometry/Triangle.hpp

Public Types

Public Member Functions

Static Public Attributes

Detailed Description

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

Member Typedef Documentation

◆ PointType

◆ VectorType

◆ SphereType

Constructor & Destructor Documentation

◆ Triangle() [1/2]

◆ Triangle() [2/2]

Member Function Documentation

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ normal()

◆ area() [1/2]

◆ area() [2/2]

◆ signedArea()

◆ volume()

◆ signedVolume()

◆ circumsphere()

◆ physToBarycentric()

◆ baryToPhysical()

◆ degenerate()

◆ checkInTriangle()

◆ angle()

◆ print()

Member Data Documentation

◆ DIM

◆ NUM_TRI_VERTS

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