This class implements a 2D triangle with Cartesian coordinates. More...

Inheritance diagram for Ocean::TriangleT2< T >:

Public Member Functions
	TriangleT2 ()=default
	Creates a new 2D triangle object with default parameters. More...

	TriangleT2 (const VectorT2< T > &point0, const VectorT2< T > &point1, const VectorT2< T > &point2)
	Creates a new 2D triangle object by three corner positions. More...

const VectorT2< T > &	point0 () const
	Returns the first triangle corner. More...

const VectorT2< T > &	point1 () const
	Returns the second triangle corner. More...

const VectorT2< T > &	point2 () const
	Returns the third triangle corner. More...

T	sqrDistance01 () const
	Returns the square distance between point0 and point1. More...

T	sqrDistance02 () const
	Returns the square distance between point0 and point2. More...

T	sqrDistance12 () const
	Returns the square distance between point1 and point2. More...

T	left () const
	Returns the most left position of this triangle. More...

T	top () const
	Returns the most top position of this triangle. More...

T	right () const
	Returns the most right position of this triangle. More...

T	bottom () const
	Returns the most bottom position of this triangle. More...

T	area () const
	Returns the area of this triangle. More...

T	area2 () const
	Returns the square area of this triangle. More...

void	cosines (T &cosine0, T &cosine1, T &cosine2) const
	Calculates the three angle cosine values of the three triangle corners. More...

void	angles (T &angle0, T &angle1, T &angle2) const
	Calculates the three angles of the three triangle corners. More...

T	minAngle () const
	Returns the minimal angle of this triangle. More...

bool	allCosineBelow (const T cosValue) const
	Returns whether all cosine values of the three triangle corners are below or equal to a given threshold. More...

T	maxSqrLength () const
	Returns the maximal square side length of this triangle. More...

T	maxLength () const
	Returns the maximal side length of this triangle. More...

T	minSqrLength () const
	Returns the minimal square side length of this triangle. More...

T	minLength () const
	Returns the minimal side length of this triangle. More...

bool	isInside (const VectorT2< T > &point) const
	Returns whether a given point lies inside this triangle. More...

bool	isCounterClockwise (const bool yAxisDownwards=true) const
	Returns whether this triangles is defined in a counter clockwise manner. More...

VectorT2< T >	barycentric2cartesian (const VectorT3< T > &barycentric) const
	Returns the 2D Cartesian coordinate of a given barycentric coordinate defined in relation to this triangle. More...

VectorT3< T >	cartesian2barycentric (const VectorT2< T > &cartesian) const
	Returns the barycentric coordinate of a given 2D Cartesian coordinate defined in relation to this triangle. More...

VectorT3< T >	barycentricCircumcenter () const
	Returns the circumcenter for this triangle in barycentric coordinates. More...

VectorT2< T >	cartesianCircumcenter () const
	Returns the circumcenter for this triangle in Cartesian coordinates. More...

VectorT3< T >	barycentricIncenter () const
	Returns the incenter for this triangle in barycentric coordinates. More...

VectorT2< T >	cartesianIncenter () const
	Returns the incenter for this triangle in Cartesian coordinates. More...

bool	intersects (const TriangleT2< T > &triangle) const
	Returns whether this triangle has an intersection with a second triangle. More...

TriangleT2< T >	padded (const T padWidth) const
	Pad a given 2D triangle along each edge by a fixed value. More...

bool	isValid () const
	Returns whether this triangle can provide valid barycentric coordinates (for 64 bit floating point values). More...

const VectorT2< T > &	operator[] (const unsigned int index) const
	Returns individual triangle corners. More...

TriangleT2< T >	operator+ (const VectorT2< T > &offset) const
	Shifts the triangle by a given 2D vector (by adding the vector to all three corners of the triangle). More...

TriangleT2< T > &	operator+= (const VectorT2< T > &offset)
	Shifts the triangle by a given 2D vector (by adding the vector to all three corners of the triangle). More...

TriangleT2< T >	operator- (const VectorT2< T > &offset) const
	Shifts the triangle by a given 2D vector (by subtracting the vector from all three corners of the triangle). More...

TriangleT2< T > &	operator-= (const VectorT2< T > &offset)
	Shifts the triangle by a given 2D vector (by subtracting the vector from all three corners of the triangle). More...

Static Public Member Functions
static bool	isInside (const std::vector< TriangleT2< T >> &triangles, const VectorT2< T > &point)
	Returns whether a given point lies inside at least one of the given triangles. More...

static T	analyzePoints (const VectorT2< T > &point0, const VectorT2< T > &point1, const VectorT2< T > &point2, const bool yAxisDownwards)
	Analyses the layout of three 2D points forming either a triangle or a line. More...

Static Public Member Functions inherited from Ocean::TriangleT< T >
static bool	isBarycentricInside (const VectorT3< T > &barycentricPoint)
	Returns whether a given point, specified as barycentric coordinate, lies inside a triangle. More...

static bool	isValidBarycentric (const VectorT3< T > &barycentric, const T &epsilon=NumericT< T >::eps())
	Returns whether the a barycentric coordinate is valid. More...

Private Attributes
VectorT2< T >	points_ [3] = {VectorT2<T>(T(0), T(0)), VectorT2<T>(T(0), T(0)), VectorT2<T>(T(0), T(0))}
	The corner positions. More...

T	barycentricFactor_ = T(0)
	Convert factor for barycentric coordinates. More...

Detailed Description

template<typename T>
class Ocean::TriangleT2< T >

This class implements a 2D triangle with Cartesian coordinates.

Template Parameters

T	Data type used to represent coordinates

See also: TriangleF2, TriangleD2, TriangleT3.

Constructor & Destructor Documentation

◆ TriangleT2() [1/2]

template<typename T >

Ocean::TriangleT2< T >::TriangleT2 ( )

default

Creates a new 2D triangle object with default parameters.

◆ TriangleT2() [2/2]

template<typename T >

Ocean::TriangleT2< T >::TriangleT2	(	const VectorT2< T > &	point0,
		const VectorT2< T > &	point1,
		const VectorT2< T > &	point2
	)

inline

Creates a new 2D triangle object by three corner positions.

Parameters

point0	First corner position
point1	Second corner position
point2	Third corner position

Member Function Documentation

◆ allCosineBelow()

template<typename T >

bool Ocean::TriangleT2< T >::allCosineBelow ( const T cosValue ) const

Returns whether all cosine values of the three triangle corners are below or equal to a given threshold.

Thus, to test whether the minimal corner angle is equal to PI/8, then allCosineBelow(cos(PI/8)) has to be checked.

Parameters

cosValue Cosine threshold value

Returns: True, if so

◆ analyzePoints()

template<typename T >

T Ocean::TriangleT2< T >::analyzePoints	(	const VectorT2< T > &	point0,
		const VectorT2< T > &	point1,
		const VectorT2< T > &	point2,
		const bool	yAxisDownwards
	)

static

Analyses the layout of three 2D points forming either a triangle or a line.

The result of the function depends on the coordinate system in which the points are defined:

First coordinate system,     Second coordinate system

 ------> x-axis              ^
|                            | y-axis
|                            |
| y-axis                     |
V                             ------> x-axis

Parameters

point0	The first point to be analyzed
point1	The first point to be analyzed
point2	The first point to be analyzed
yAxisDownwards	True, if the y-axis points downwards and x-axis points to the right; False, if the y-axis points upwards and the x-axis points to the right

Returns: A negative value if the three points define a counter clockwise triangle, a positive value for a clockwise triangle, zero is the tree points are located on a line, with range (-infinity, infinity)

◆ angles()

template<typename T >

void Ocean::TriangleT2< T >::angles	(	T &	angle0,
		T &	angle1,
		T &	angle2
	)		const

inline

Calculates the three angles of the three triangle corners.

Beware: Make sure that this triangle is valid before!

Parameters

angle0	Resulting angle corresponding to point0 in radian
angle1	Resulting angle corresponding to point1 in radian
angle2	Resulting angle corresponding to point2 in radian

◆ area()

template<typename T >

T Ocean::TriangleT2< T >::area

inline

Returns the area of this triangle.

Returns: Triangle area

See also: area2().

◆ area2()

template<typename T >

T Ocean::TriangleT2< T >::area2

inline

Returns the square area of this triangle.

Returns: Triangle area

See also: area().

◆ barycentric2cartesian()

template<typename T >

VectorT2< T > Ocean::TriangleT2< T >::barycentric2cartesian ( const VectorT3< T > & barycentric ) const

inline

Returns the 2D Cartesian coordinate of a given barycentric coordinate defined in relation to this triangle.

Parameters

barycentric The Barycentric coordinate to convert to a Cartesian coordinate

Returns: Cartesian coordinate

◆ barycentricCircumcenter()

template<typename T >

VectorT3< T > Ocean::TriangleT2< T >::barycentricCircumcenter

Returns the circumcenter for this triangle in barycentric coordinates.

Returns: Barycentric coordinates of the circumcenter

◆ barycentricIncenter()

template<typename T >

VectorT3< T > Ocean::TriangleT2< T >::barycentricIncenter

Returns the incenter for this triangle in barycentric coordinates.

Returns: Barycentric coordinates of the incenter

◆ bottom()

template<typename T >

T Ocean::TriangleT2< T >::bottom

inline

Returns the most bottom position of this triangle.

Returns: Bottom position

◆ cartesian2barycentric()

template<typename T >

VectorT3< T > Ocean::TriangleT2< T >::cartesian2barycentric ( const VectorT2< T > & cartesian ) const

inline

Returns the barycentric coordinate of a given 2D Cartesian coordinate defined in relation to this triangle.

Parameters

cartesian The Cartesian coordinate to convert to a barycentric coordinate

Returns: Barycentric coordinate

◆ cartesianCircumcenter()

template<typename T >

VectorT2< T > Ocean::TriangleT2< T >::cartesianCircumcenter

inline

Returns the circumcenter for this triangle in Cartesian coordinates.

Returns: Cartesian coordinates of the circumcenter

◆ cartesianIncenter()

template<typename T >

VectorT2< T > Ocean::TriangleT2< T >::cartesianIncenter

inline

Returns the incenter for this triangle in Cartesian coordinates.

Returns: Cartesian coordinates of the circumcenter

◆ cosines()

template<typename T >

void Ocean::TriangleT2< T >::cosines	(	T &	cosine0,
		T &	cosine1,
		T &	cosine2
	)		const

Calculates the three angle cosine values of the three triangle corners.

Beware: Make sure that this triangle is valid before!

Parameters

cosine0	Resulting angle corresponding to point0
cosine1	Resulting angle corresponding to point1
cosine2	Resulting angle corresponding to point2

◆ intersects()

template<typename T >

bool Ocean::TriangleT2< T >::intersects ( const TriangleT2< T > & triangle ) const

Returns whether this triangle has an intersection with a second triangle.

Parameters

triangle The second triangle to test

Returns: True, if so

◆ isCounterClockwise()

template<typename T >

bool Ocean::TriangleT2< T >::isCounterClockwise ( const bool yAxisDownwards = true ) const

inline

Returns whether this triangles is defined in a counter clockwise manner.

The result of the function depends on the coordinate system in which the points are defined:

First coordinate system,     Second coordinate system

 ------> x-axis              ^
|                            | y-axis
|                            |
| y-axis                     |
V                             ------> x-axis

Parameters

yAxisDownwards True, if the y-axis points downwards and x-axis points to the right; False, if the y-axis points upwards and the x-axis points to the right

Returns: True, if so

◆ isInside() [1/2]

template<typename T >

bool Ocean::TriangleT2< T >::isInside	(	const std::vector< TriangleT2< T >> &	triangles,
		const VectorT2< T > &	point
	)

inlinestatic

Returns whether a given point lies inside at least one of the given triangles.

Parameters

triangles	The triangles that are tested
point	The point to be checked

Returns: True, if so

◆ isInside() [2/2]

template<typename T >

bool Ocean::TriangleT2< T >::isInside ( const VectorT2< T > & point ) const

inline

Returns whether a given point lies inside this triangle.

Parameters

point The point to be checked

Returns: True, if so

◆ isValid()

template<typename T >

bool Ocean::TriangleT2< T >::isValid

inline

Returns whether this triangle can provide valid barycentric coordinates (for 64 bit floating point values).

For 32 bit floating point values we simply check whether all three corners of the triangle are different.

Returns: True, if so

◆ left()

template<typename T >

T Ocean::TriangleT2< T >::left

inline

Returns the most left position of this triangle.

Returns: Left position

◆ maxLength()

template<typename T >

T Ocean::TriangleT2< T >::maxLength

inline

Returns the maximal side length of this triangle.

Returns: Maximal side length

◆ maxSqrLength()

template<typename T >

T Ocean::TriangleT2< T >::maxSqrLength

inline

Returns the maximal square side length of this triangle.

Returns: Maximal square side length

◆ minAngle()

template<typename T >

T Ocean::TriangleT2< T >::minAngle

inline

Returns the minimal angle of this triangle.

Beware: Make sure that this triangle is valid before!

Returns: Minimal angle in radian

◆ minLength()

template<typename T >

T Ocean::TriangleT2< T >::minLength

inline

Returns the minimal side length of this triangle.

Returns: Minimal side length

◆ minSqrLength()

template<typename T >

T Ocean::TriangleT2< T >::minSqrLength

inline

Returns the minimal square side length of this triangle.

Returns: Minimal square side length

◆ operator+()

template<typename T >

TriangleT2< T > Ocean::TriangleT2< T >::operator+ ( const VectorT2< T > & offset ) const

inline

Shifts the triangle by a given 2D vector (by adding the vector to all three corners of the triangle).

Parameters

offset The offset vector to shift the triangle

Returns: The new shifted triangle

◆ operator+=()

template<typename T >

TriangleT2< T > & Ocean::TriangleT2< T >::operator+= ( const VectorT2< T > & offset )

inline

Shifts the triangle by a given 2D vector (by adding the vector to all three corners of the triangle).

Parameters

offset The offset vector to shift the triangle

Returns: The reference to this triangle

◆ operator-()

template<typename T >

TriangleT2< T > Ocean::TriangleT2< T >::operator- ( const VectorT2< T > & offset ) const

inline

Shifts the triangle by a given 2D vector (by subtracting the vector from all three corners of the triangle).

Parameters

offset The offset vector to shift the triangle

Returns: The new shifted triangle

◆ operator-=()

template<typename T >

TriangleT2< T > & Ocean::TriangleT2< T >::operator-= ( const VectorT2< T > & offset )

inline

Shifts the triangle by a given 2D vector (by subtracting the vector from all three corners of the triangle).

Parameters

offset The offset vector to shift the triangle

Returns: The reference to this triangle

◆ operator[]()

template<typename T >

const VectorT2< T > & Ocean::TriangleT2< T >::operator[] ( const unsigned int index ) const

inline

Returns individual triangle corners.

Parameters

index Index of the corner that is requested, with range [0, 2]

Returns: Resulting triangle corner

◆ padded()

template<typename T >

TriangleT2< T > Ocean::TriangleT2< T >::padded ( const T padWidth ) const

Pad a given 2D triangle along each edge by a fixed value.

For a positive pad width, each side of the resulting triangle is shifted away from the triangle circumcenter along the perpendicular.

Parameters

padWidth Absolute amount to shift the triangle edges out from the triangle circumcenter, with range (-infinity, infinity); note that, in the case where the padding is negative with an absolute value smaller than the shortest distance from the circumcenter to an edge, then the triangle will flip its orientation

Returns: Padded 2D triangle

◆ point0()

template<typename T >

const VectorT2< T > & Ocean::TriangleT2< T >::point0

inline

Returns the first triangle corner.

Returns: First triangle corner

◆ point1()

template<typename T >

const VectorT2< T > & Ocean::TriangleT2< T >::point1

inline

Returns the second triangle corner.

Returns: Second triangle corner

◆ point2()

template<typename T >

const VectorT2< T > & Ocean::TriangleT2< T >::point2

inline

Returns the third triangle corner.

Returns: Third triangle corner

◆ right()

template<typename T >

T Ocean::TriangleT2< T >::right

inline

Returns the most right position of this triangle.

Returns: Right position

◆ sqrDistance01()

template<typename T >

T Ocean::TriangleT2< T >::sqrDistance01

inline

Returns the square distance between point0 and point1.

Returns: Square distance

◆ sqrDistance02()

template<typename T >

T Ocean::TriangleT2< T >::sqrDistance02

inline

Returns the square distance between point0 and point2.

Returns: Square distance

◆ sqrDistance12()

template<typename T >

T Ocean::TriangleT2< T >::sqrDistance12

inline

Returns the square distance between point1 and point2.

Returns: Square distance

◆ top()

template<typename T >

T Ocean::TriangleT2< T >::top

inline

Returns the most top position of this triangle.

Returns: Top position

Field Documentation

◆ barycentricFactor_

template<typename T >

T Ocean::TriangleT2< T >::barycentricFactor_ = T(0)

private

Convert factor for barycentric coordinates.

◆ points_

template<typename T >

VectorT2<T> Ocean::TriangleT2< T >::points_[3] = {VectorT2<T>(T(0), T(0)), VectorT2<T>(T(0), T(0)), VectorT2<T>(T(0), T(0))}

private

The corner positions.

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

Triangle2.h

Public Member Functions

Static Public Member Functions

Private Attributes

Detailed Description

template<typename T> class Ocean::TriangleT2< T >

Constructor & Destructor Documentation

◆ TriangleT2() [1/2]

◆ TriangleT2() [2/2]

Member Function Documentation

◆ allCosineBelow()

◆ analyzePoints()

◆ angles()

◆ area()

◆ area2()

◆ barycentric2cartesian()

◆ barycentricCircumcenter()

◆ barycentricIncenter()

◆ bottom()

◆ cartesian2barycentric()

◆ cartesianCircumcenter()

◆ cartesianIncenter()

◆ cosines()

◆ intersects()

◆ isCounterClockwise()

◆ isInside() [1/2]

◆ isInside() [2/2]

◆ isValid()

◆ left()

◆ maxLength()

◆ maxSqrLength()

◆ minAngle()

◆ minLength()

◆ minSqrLength()

◆ operator+()

◆ operator+=()

◆ operator-()

◆ operator-=()

◆ operator[]()

◆ padded()

◆ point0()

◆ point1()

◆ point2()

◆ right()

◆ sqrDistance01()

◆ sqrDistance02()

◆ sqrDistance12()

◆ top()

Field Documentation

◆ barycentricFactor_

◆ points_

template<typename T>
class Ocean::TriangleT2< T >