A 3-dimensional triangle and related functions. More...

#include <gz/math/Triangle3.hh>

Public Member Functions
	Triangle3 ()=default
	Default constructor. More...

	Triangle3 (const Vector3< T > &_pt1, const Vector3< T > &_pt2, const Vector3< T > &_pt3)
	Constructor. More...

double	Area () const
	Get the area of this triangle. More...

bool	Contains (const Line3< T > &_line) const
	Check if this triangle completely contains the given line segment. More...

bool	Contains (const Vector3< T > &_pt) const
	Get whether this triangle contains the given point. More...

bool	Intersects (const Line3< T > &_line, Vector3< T > &_ipt1) const
	Get whether the given line intersects an edge of this triangle. More...

Vector3d	Normal () const
	Get the triangle's normal vector. More...

Vector3< T >	operator[] (const size_t _index) const
	Get one of points that define the triangle. More...

T	Perimeter () const
	Get the length of the triangle's perimeter. More...

void	Set (const unsigned int _index, const Vector3< T > &_pt)
	Set one vertex of the triangle. More...

void	Set (const Vector3< T > &_pt1, const Vector3< T > &_pt2, const Vector3< T > &_pt3)
	Set all vertices of the triangle. More...

Line3< T >	Side (const unsigned int _index) const
	Get a line segment for one side of the triangle. More...

bool	Valid () const
	Get whether this triangle is valid, based on triangle inequality: the sum of the lengths of any two sides must be greater than the length of the remaining side. More...

Detailed Description

template<typename T>
class gz::math::Triangle3< T >

A 3-dimensional triangle and related functions.

Constructor & Destructor Documentation

◆ Triangle3() [1/2]

Triangle3 ( )

default

Default constructor.

◆ Triangle3() [2/2]

Triangle3	(	const Vector3< T > &	_pt1,
		const Vector3< T > &	_pt2,
		const Vector3< T > &	_pt3
	)

inline

Constructor.

Keep in mind that the triangle normal is determined by the order of these vertices. Search the internet for "triangle winding" for more information.

Parameters

[in]	_pt1	First point that defines the triangle.
[in]	_pt2	Second point that defines the triangle.
[in]	_pt3	Third point that defines the triangle.

References Triangle3< T >::Set().

Member Function Documentation

◆ Area()

double Area ( ) const

inline

Get the area of this triangle.

Returns: Triangle's area.

References Triangle3< T >::Perimeter(), and Triangle3< T >::Side().

◆ Contains() [1/2]

bool Contains ( const Line3< T > & _line ) const

inline

Check if this triangle completely contains the given line segment.

Parameters

[in] _line Line to check.

Returns: True if the line's start and end points are both inside this triangle.

Referenced by Triangle3< T >::Intersects().

◆ Contains() [2/2]

bool Contains ( const Vector3< T > & _pt ) const

inline

Get whether this triangle contains the given point.

Parameters

[in] _pt Point to check.

Returns: True if the point is inside or on the triangle.

References Vector3< T >::Dot(), Plane< T >::NO_SIDE, Triangle3< T >::Normal(), and Triangle3< T >::Side().

◆ Intersects()

bool Intersects	(	const Line3< T > &	_line,
		Vector3< T > &	_ipt1
	)		const

inline

Get whether the given line intersects an edge of this triangle.

The returned intersection point is one of:

If the line is coplanar with the triangle:
- The point on the closest edge of the triangle that the line intersects. OR
- The first point on the line, if the line is completely contained
If the line is not coplanar, the point on the triangle that the line intersects.

Parameters

[in]	_line	Line to check.
[out]	_ipt1	Return value of the first intersection point, only valid if the return value of the function is true.

Returns: True if the given line intersects this triangle.

References Triangle3< T >::Contains(), Vector3< T >::Dot(), gz::math::equal(), Line3< T >::Intersect(), Line3< T >::Length(), and Triangle3< T >::Normal().

◆ Normal()

Vector3d Normal ( ) const

inline

Get the triangle's normal vector.

Returns: The normal vector for the triangle.

References Vector3< T >::Normal().

Referenced by Triangle3< T >::Contains(), and Triangle3< T >::Intersects().

◆ operator[]()

Vector3<T> operator[] ( const size_t _index ) const

inline

Get one of points that define the triangle.

Parameters

[in] _index 0, 1, or 2. _index is clamped to the range [0,2].

Returns: The triangle point at _index.

References gz::math::clamp(), gz::math::GZ_TWO_SIZE_T, and gz::math::GZ_ZERO_SIZE_T.

◆ Perimeter()

T Perimeter ( ) const

inline

Get the length of the triangle's perimeter.

Returns: Sum of the triangle's line segments.

References Triangle3< T >::Side().

Referenced by Triangle3< T >::Area().

◆ Set() [1/2]

void Set	(	const unsigned int	_index,
		const Vector3< T > &	_pt
	)

inline

Set one vertex of the triangle.

Keep in mind that the triangle normal is determined by the order of these vertices. Search the internet for "triangle winding" for more information.

Parameters

[in]	_index	Index of the point to set. _index is clamped to the range [0,2].
[in]	_pt	Value of the point to set.

References gz::math::clamp().

Referenced by Triangle3< T >::Triangle3().

◆ Set() [2/2]

void Set	(	const Vector3< T > &	_pt1,
		const Vector3< T > &	_pt2,
		const Vector3< T > &	_pt3
	)

inline

Set all vertices of the triangle.

Keep in mind that the triangle normal is determined by the order of these vertices. Search the internet for "triangle winding" for more information.

Parameters

[in]	_pt1	First point that defines the triangle.
[in]	_pt2	Second point that defines the triangle.
[in]	_pt3	Third point that defines the triangle.

◆ Side()

Line3<T> Side ( const unsigned int _index ) const

inline

Get a line segment for one side of the triangle.

Parameters

[in] _index Index of the side to retrieve, where 0 == Line3(pt1, pt2), 1 == Line3(pt2, pt3), 2 == Line3(pt3, pt1). _index is clamped to the range [0,2].

Returns: Line segment of the requested side.

Referenced by Triangle3< T >::Area(), Triangle3< T >::Contains(), Triangle3< T >::Perimeter(), and Triangle3< T >::Valid().

◆ Valid()

bool Valid ( ) const

inline

Get whether this triangle is valid, based on triangle inequality: the sum of the lengths of any two sides must be greater than the length of the remaining side.

Returns: True if the triangle inequality holds

References Triangle3< T >::Side().

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

gz/math/Triangle3.hh

Gazebo Math

API Reference

Public Member Functions

Detailed Description

template<typename T>
class gz::math::Triangle3< T >

Constructor & Destructor Documentation

◆ Triangle3() [1/2]

◆ Triangle3() [2/2]

Member Function Documentation

◆ Area()

◆ Contains() [1/2]

◆ Contains() [2/2]

◆ Intersects()

◆ Normal()

◆ operator[]()

◆ Perimeter()

◆ Set() [1/2]

◆ Set() [2/2]

◆ Side()

◆ Valid()

Public Member Functions

Detailed Description

template<typename T> class gz::math::Triangle3< T >

Constructor & Destructor Documentation

◆ Triangle3() [1/2]

◆ Triangle3() [2/2]

Member Function Documentation

◆ Area()

◆ Contains() [1/2]

◆ Contains() [2/2]

◆ Intersects()

◆ Normal()

◆ operator[]()

◆ Perimeter()

◆ Set() [1/2]

◆ Set() [2/2]

◆ Side()

◆ Valid()

template<typename T>
class gz::math::Triangle3< T >