EBGeometry::Triangle2D< T > Class Template Reference

Class for embedding a triangle face into 2D. More...

#include <EBGeometry_Triangle2D.hpp>

Public Types
enum class	InsideOutsideAlgorithm { SubtendedAngle , CrossingNumber , WindingNumber }
	Supported algorithms for performing inside/outside tests when checking if a point projects to the inside or outside of a polygon face.
using	Vec2 = Vec2T< T >
	Alias for 2D vector type.
using	Vec3 = Vec3T< T >
	Alias for 3D vector type.

Public Member Functions
	Triangle2D () noexcept=default
	Default constructor. Must subsequently call the define function.
	Triangle2D (const Vec3 &a_normal, const std::array< Vec3, 3 > &a_vertices) noexcept
	Full constructor.
	Triangle2D (const Triangle2D &a_triangle2D) noexcept=default
	Copy constructor.
	Triangle2D (Triangle2D &&a_triangle2D) noexcept=default
	Move constructor.
	~Triangle2D () noexcept=default
	Destructor (does nothing)
Triangle2D &	operator= (const Triangle2D &a_triangle2D) noexcept=default
	Copy assignment.
Triangle2D &	operator= (Triangle2D &&a_triangle2D) noexcept=default
	Move assignment.
void	define (const Vec3 &a_normal, const std::array< Vec3, 3 > &a_vertices) noexcept
	Define function. Puts object in usable state.
bool	isPointInside (const Vec3 &a_point, InsideOutsideAlgorithm a_algorithm) const noexcept
	Check if a point is inside or outside the 2D polygon.
bool	isPointInsideWindingNumber (const Vec3 &a_point) const noexcept
	Check if a point is inside a 2D polygon, using the winding number algorithm.
bool	isPointInsideCrossingNumber (const Vec3 &a_point) const noexcept
	Check if a point is inside a 2D polygon, by computing the number of times a ray crosses the polygon edges.
bool	isPointInsideSubtend (const Vec3 &a_point) const noexcept
	Check if a point is inside a 2D polygon, using the subtended angles.

Detailed Description

template<class T>
class EBGeometry::Triangle2D< T >

Class for embedding a triangle face into 2D.

This class is required for determining whether or not a 3D point projected to the plane of a triangle lies inside or outside the triangle. To do this we compute the 2D embedding of the triangle face, reducing the problem to a tractable dimension where we can use well-tested algorithm. Once the 2D embedding is computed, we can use well-known algorithms for checking if a point lies inside or outside. The supported algorithms are 1) The winding number algorithm (computing the winding number), 2) Computing the subtended angle of the point with the edges of the polygon (sums to 360 degrees if the point is inside), or computing the crossing number which checks how many times a ray cast from the point crosses the edges of the triangle.

Constructor & Destructor Documentation

Triangle2D() [1/3]

template<class T >

EBGeometry::Triangle2D< T >::Triangle2D ( const Vec3 &  a_normal, const std::array< Vec3, 3 > &  a_vertices  )

noexcept

Full constructor.

Parameters

[in]	a_normal	Normal vector of the 3D triangle
[in]	a_vertices	Vertex coordinates of the 3D triangle

Triangle2D() [2/3]

template<class T >

EBGeometry::Triangle2D< T >::Triangle2D ( const Triangle2D< T > &  a_triangle2D )

defaultnoexcept

Copy constructor.

Parameters

[in]

a_triangle2D

Other triangle

Triangle2D() [3/3]

template<class T >

EBGeometry::Triangle2D< T >::Triangle2D ( Triangle2D< T > &&  a_triangle2D )

defaultnoexcept

Move constructor.

Parameters

[in,out]

a_triangle2D

Other triangle

Member Function Documentation

define()

template<class T >

void EBGeometry::Triangle2D< T >::define ( const Vec3 &  a_normal, const std::array< Vec3, 3 > &  a_vertices  )

noexcept

Define function. Puts object in usable state.

Parameters

[in]	a_normal	Normal vector of the 3D triangle
[in]	a_vertices	Vertex coordinates of the 3D triangle

isPointInside()

template<class T >

bool EBGeometry::Triangle2D< T >::isPointInside ( const Vec3 &  a_point, InsideOutsideAlgorithm  a_algorithm  ) const

noexcept

Check if a point is inside or outside the 2D polygon.

Parameters

[in]	a_point	3D point coordinates
[in]	a_algorithm	Inside/outside algorithm

This will call the function corresponding to a_algorithm.

isPointInsideCrossingNumber()

template<class T >

bool EBGeometry::Triangle2D< T >::isPointInsideCrossingNumber ( const Vec3 &  a_point ) const

noexcept

Check if a point is inside a 2D polygon, by computing the number of times a ray crosses the polygon edges.

Parameters

[in]

a_point

3D point coordinates

Returns

Returns true if the 3D point projects to the inside of the 2D polygon

isPointInsideSubtend()

template<class T >

bool EBGeometry::Triangle2D< T >::isPointInsideSubtend ( const Vec3 &  a_point ) const

noexcept

Check if a point is inside a 2D polygon, using the subtended angles.

Parameters

[in]

a_point

3D point coordinates

Returns

Returns true if the 3D point projects to the inside of the 2D polygon

isPointInsideWindingNumber()

template<class T >

bool EBGeometry::Triangle2D< T >::isPointInsideWindingNumber ( const Vec3 &  a_point ) const

noexcept

Check if a point is inside a 2D polygon, using the winding number algorithm.

Parameters

[in]

a_point

3D point coordinates

Returns

Returns true if the 3D point projects to the inside of the 2D polygon

operator=() [1/2]

template<class T >

Triangle2D & EBGeometry::Triangle2D< T >::operator= ( const Triangle2D< T > &  a_triangle2D )

defaultnoexcept

Copy assignment.

Parameters

[in]

a_triangle2D

Other triangle

operator=() [2/2]

template<class T >

Triangle2D & EBGeometry::Triangle2D< T >::operator= ( Triangle2D< T > &&  a_triangle2D )

defaultnoexcept

Move assignment.

Parameters

[in,out]

a_triangle2D

Other triangle

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

• /home/runner/work/EBGeometry/EBGeometry/Source/EBGeometry_Triangle2D.hpp