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

#include </home/docs/checkouts/readthedocs.org/user_builds/axom/checkouts/v0.5.0/src/axom/primal/geometry/Triangle.hpp>

Public Types
enum	{ NUM_TRI_VERTS = 3 }

typedef Point< T, NDIMS >	PointType

typedef Vector< T, NDIMS >	VectorType

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	~Triangle ()
	Destructor. 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 VectorType	normal () const
	Returns the normal of the triangle (not normalized) More...

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

Point< double, 3 >	physToBarycentric (const PointType &p) 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=1.0e-8) const
	Returns whether Point P is in the triangle for some 3d Triangle. More...

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...

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>

typedef Point<T, NDIMS> axom::primal::Triangle< T, NDIMS >::PointType

◆ VectorType

template<typename T, int NDIMS>

typedef Vector<T, NDIMS> axom::primal::Triangle< T, NDIMS >::VectorType

Member Enumeration Documentation

◆ anonymous enum

template<typename T, int NDIMS>

anonymous enum

Enumerator
NUM_TRI_VERTS

Constructor & Destructor Documentation

◆ Triangle() [1/2]

template<typename T , int NDIMS>

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

Default constructor. Creates a degenerate triangle.

◆ Triangle() [2/2]

template<typename T , int NDIMS>

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

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.

References A, and B.

◆ ~Triangle()

template<typename T, int NDIMS>

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

inline

Destructor.

References AXOM_HOST_DEVICE.

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

◆ normal()

template<typename T, int NDIMS>

AXOM_HOST_DEVICE VectorType 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_HOST_DEVICE, axom::primal::Vector< T, NDIMS >::cross_product(), and SLIC_CHECK_MSG.

◆ area()

template<typename T, int NDIMS>

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

inline

Returns the area of the triangle.

Precondition: Only defined when dimension NDIMS is 2 or 3

References A, B, C, axom::primal::Vector< T, NDIMS >::cross_product(), and SLIC_CHECK_MSG.

Referenced by axom::primal::Triangle< T, NDIMS >::degenerate().

◆ physToBarycentric()

template<typename T, int NDIMS>

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

inline

Returns the barycentric coordinates of a point within a triangle.

Returns: The barycentric coordinates of the triangle inside a Point<T,3>

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

Postcondition: The barycentric coordinates sum to 1. Adapted from Real Time Collision Detection by Christer Ericson.

References A, axom::utilities::abs(), B, C, axom::primal::Vector< T, NDIMS >::cross_product(), axom::numerics::determinant(), axom::utilities::isNearlyEqual(), and SLIC_CHECK.

Referenced by axom::primal::Triangle< T, NDIMS >::checkInTriangle().

◆ 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_HOST_DEVICE, axom::utilities::isNearlyEqual(), 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().

Referenced by axom::quest::getMeshTriangle().

◆ checkInTriangle()

template<typename T, int NDIMS>

bool axom::primal::Triangle< T, NDIMS >::checkInTriangle	(	const PointType &	p,
		double	eps = `1.0e-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::primal::Triangle< T, NDIMS >::angle(), axom::utilities::isNearlyEqual(), and axom::primal::Triangle< T, NDIMS >::physToBarycentric().

◆ angle()

template<typename T , int NDIMS>

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::primal::Vector< T, NDIMS >::dot_product(), axom::primal::Vector< T, NDIMS >::norm(), axom::primal::Triangle< T, NDIMS >::NUM_TRI_VERTS, and SLIC_ASSERT.

Referenced by axom::primal::Triangle< T, NDIMS >::checkInTriangle().

◆ 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

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

/home/docs/checkouts/readthedocs.org/user_builds/axom/checkouts/v0.5.0/src/axom/primal/geometry/Triangle.hpp

Public Types

Public Member Functions

Detailed Description

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

Member Typedef Documentation

◆ PointType

◆ VectorType

Member Enumeration Documentation

◆ anonymous enum

Constructor & Destructor Documentation

◆ Triangle() [1/2]

◆ Triangle() [2/2]

◆ ~Triangle()

Member Function Documentation

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ normal()

◆ area()

◆ physToBarycentric()

◆ baryToPhysical()

◆ degenerate()

◆ checkInTriangle()

◆ angle()

◆ print()

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