Public Types
using	ScalarType = PointT::ScalarType

using	PointType = PointT

Public Member Functions
	Triangle (const PointT &p0, const PointT &p1, const PointT &p2)

constexpr uint	size () const
	Returns the number of points of the triangle.

const PointT &	point (uint i) const
	Returns the i-th point of the triangle.

PointT &	point (uint i)

PointT &	point0 ()

const PointT &	point0 () const

PointT &	point1 ()

const PointT &	point1 () const

PointT &	point2 ()

const PointT &	point2 () const

ScalarType	sideLength (uint i) const
	Returns the length of the i-th side of the triangle.

ScalarType	sideLength0 () const
	Returns the length of the first side of the triangle.

ScalarType	sideLength1 () const
	Returns the length of the second side of the triangle.

ScalarType	sideLength2 () const
	Returns the length of the third side of the triangle.

PointT	normal () const
	Returns the normal of the triangle.

PointT	barycenter () const
	Computes the barycenter of the triangle.

PointT	weightedBarycenter (ScalarType w0, ScalarType w1, ScalarType w2) const
	Computes the weighted barycenter of the triangle.

PointT	weightedBarycenter (const Point3< ScalarType > &w) const
	Computes the weighted barycenter of the triangle.

PointT	barycentricCoordinatePoint (ScalarType b0, ScalarType b1, ScalarType b2) const

PointT	barycentricCoordinatePoint (const Point3< ScalarType > &b) const
	Computes the point in the triangle with the given barycentric coordinates.

PointT	circumcenter () const
	Compute the circumcenter of the triangle.

ScalarType	perimeter () const
	Computes the perimeter of the triangle.

ScalarType	area () const
	Computes the area of the triangle.

ScalarType	quality () const
	Calculates the quality measure of the triangle.

ScalarType	qualityRadii () const
	Compute a shape quality measure of the triangle.

ScalarType	qualityMeanRatio () const
	Compute the mean ratio of the triangle shape quality measure.

ScalarType	sideLength (const PointT &p0, const PointT &p1, const PointT &p2, uint i) const
	Returns the length of the i-th side of the triangle composed by the points `p0`, `p1`, and `p2`.

Static Public Member Functions
static PointT	normal (const PointT &p0, const PointT &p1, const PointT &p2)
	Computes the normal of the triangle composed by the 3D points `p0`, `p1`, and `p2`, considering that these three points are ordered in counter-clockwise order.

static PointT	barycenter (const PointT &p0, const PointT &p1, const PointT &p2)
	Computes the barycenter of the triangle composed by the points `p0`, `p1`, and `p2`.

static PointT	weightedBarycenter (const PointT &p0, const PointT &p1, const PointT &p2, ScalarType w0, ScalarType w1, ScalarType w2)
	Computes the weighted barycenter of a triangle composed of three points.

static PointT	barycentricCoordinatePoint (const PointT &p0, const PointT &p1, const PointT &p2, ScalarType b0, ScalarType b1, ScalarType b2)
	Computes the point in a triangle with the given barycentric coordinates.

static PointT	circumcenter (const PointT &p0, const PointT &p1, const PointT &p2)
	Compute the circumcenter of a triangle.

static ScalarType	perimeter (const PointT &p0, const PointT &p1, const PointT &p2)
	Computes the perimeter of the triangle composed by the points `p0`, `p1`, and `p2`.

static ScalarType	area (const PointT &p0, const PointT &p1, const PointT &p2)
	Computes the area of the triangle composed by the points `p0`, `p1`, and `p2`, considering that these three points are ordered in counterclockwise order.

static ScalarType	quality (const PointT &p0, const PointT &p1, const PointT &p2)
	Calculates the quality measure of a triangle, given its three vertices.

static ScalarType	qualityRadii (const PointT &p0, const PointT &p1, const PointT &p2)
	Compute a shape quality measure of the triangle composed by points `p0`, `p1`, `p2`.

static ScalarType	qualityMeanRatio (const PointT &p0, const PointT &p1, const PointT &p2)
	Compute the mean ratio of a triangle shape quality measure.

Static Public Attributes
static const uint	DIM = PointT::DIM

Private Attributes
std::array< PointT, 3 >	mPoints

Member Function Documentation

◆ area() [1/2]

template<PointConcept PointT>

ScalarType vcl::Triangle< PointT >::area ( ) const

inline

Computes the area of the triangle.

Returns: The area of the triangle.

◆ area() [2/2]

template<PointConcept PointT>

static ScalarType vcl::Triangle< PointT >::area	(	const PointT &	p0,
		const PointT &	p1,
		const PointT &	p2
	)

inlinestatic

Computes the area of the triangle composed by the points p0, p1, and p2, considering that these three points are ordered in counterclockwise order.

Parameters

[in]	p0	First point of the triangle.
[in]	p1	Second point of the triangle.
[in]	p2	Third point of the triangle.

Returns: The area of the triangle composed by p0, p1, and p2.

◆ barycenter() [1/2]

template<PointConcept PointT>

PointT vcl::Triangle< PointT >::barycenter ( ) const

inline

Computes the barycenter of the triangle.

Returns: The barycenter of the triangle.

◆ barycenter() [2/2]

template<PointConcept PointT>

static PointT vcl::Triangle< PointT >::barycenter	(	const PointT &	p0,
		const PointT &	p1,
		const PointT &	p2
	)

inlinestatic

Computes the barycenter of the triangle composed by the points p0, p1, and p2.

Parameters

[in]	p0	first point of the triangle.
[in]	p1	second point of the triangle.
[in]	p2	third point of the triangle.

Returns: The barycenter of the triangle composed by p0, p1 and p2.

◆ barycentricCoordinatePoint() [1/2]

template<PointConcept PointT>

PointT vcl::Triangle< PointT >::barycentricCoordinatePoint ( const Point3< ScalarType > & b ) const

inline

Computes the point in the triangle with the given barycentric coordinates.

Given a set of barycentric coordinates b, this function computes the point in the triangle corresponding to those barycentric coordinates.

Parameters

[in] b The barycentric coordinates of the point in the triangle of type Point3<ScalarType>.

Returns: The point in the triangle corresponding to the given barycentric coordinates.

◆ barycentricCoordinatePoint() [2/2]

template<PointConcept PointT>

static PointT vcl::Triangle< PointT >::barycentricCoordinatePoint	(	const PointT &	p0,
		const PointT &	p1,
		const PointT &	p2,
		ScalarType	b0,
		ScalarType	b1,
		ScalarType	b2
	)

inlinestatic

Computes the point in a triangle with the given barycentric coordinates.

Given a triangle with vertices p0, p1, and p2, and a set of barycentric coordinates b0, b1 and b2, this function computes the point in the triangle corresponding to those barycentric coordinates.

Parameters

[in]	p0	The first vertex of the triangle.
[in]	p1	The second vertex of the triangle.
[in]	p2	The third vertex of the triangle.
[in]	b0	The first barycentric coordinate of the point in the triangle.
[in]	b1	The first barycentric coordinate of the point in the triangle.
[in]	b2	The first barycentric coordinate of the point in the triangle.

Returns: The point in the triangle corresponding to the given barycentric coordinates.

◆ circumcenter() [1/2]

template<PointConcept PointT>

PointT vcl::Triangle< PointT >::circumcenter ( ) const

inline

Compute the circumcenter of the triangle.

The function computes the circumcenter of the triangle, which is the center of the circle that passes through the three vertices of the triangle. The circumcenter is defined as the intersection of the perpendicular bisectors of the three sides of the triangle.

Returns: The circumcenter of the triangle.

Note: The function assumes that the three points are not collinear and form a valid triangle.

◆ circumcenter() [2/2]

template<PointConcept PointT>

static PointT vcl::Triangle< PointT >::circumcenter	(	const PointT &	p0,
		const PointT &	p1,
		const PointT &	p2
	)

inlinestatic

Compute the circumcenter of a triangle.

Given three points p0, p1, p2 representing a triangle, the function computes the circumcenter of the triangle, which is the center of the circle that passes through the three vertices of the triangle. The circumcenter is defined as the intersection of the perpendicular bisectors of the three sides of the triangle.

Template Parameters

PointType A type that satisfies the PointConcept.

Parameters

[in]	p0	The first point of the triangle.
[in]	p1	The second point of the triangle.
[in]	p2	The third point of the triangle.

Returns: The circumcenter of the triangle.

Note: The function assumes that the three points are not collinear and form a valid triangle.

◆ normal() [1/2]

template<PointConcept PointT>

PointT vcl::Triangle< PointT >::normal ( ) const

inline

Returns the normal of the triangle.

Note: This function is available only if the dimension of the triangle is 3.

Returns: The ormal of the triangle.

◆ normal() [2/2]

template<PointConcept PointT>

static PointT vcl::Triangle< PointT >::normal	(	const PointT &	p0,
		const PointT &	p1,
		const PointT &	p2
	)

inlinestatic

Computes the normal of the triangle composed by the 3D points p0, p1, and p2, considering that these three points are ordered in counter-clockwise order.

Template Parameters

PointType A type that satisfies the PointConcept.

Parameters

[in]	p0	first point of the triangle.
[in]	p1	second point of the triangle.
[in]	p2	third point of the triangle.

Returns: The normal of the triangle composed by p0, p1 and p2.

◆ perimeter() [1/2]

template<PointConcept PointT>

ScalarType vcl::Triangle< PointT >::perimeter ( ) const

inline

Computes the perimeter of the triangle.

Returns: The perimeter of the triangle.

◆ perimeter() [2/2]

template<PointConcept PointT>

static ScalarType vcl::Triangle< PointT >::perimeter	(	const PointT &	p0,
		const PointT &	p1,
		const PointT &	p2
	)

inlinestatic

Computes the perimeter of the triangle composed by the points p0, p1, and p2.

Parameters

[in]	p0	first point of the triangle.
[in]	p1	second point of the triangle.
[in]	p2	third point of the triangle.

Returns: The perimeter of the triangle composed by p0, p1, and p2.

◆ point()

template<PointConcept PointT>

const PointT & vcl::Triangle< PointT >::point ( uint i ) const

inline

Returns the i-th point of the triangle.

Parameters

[in] i Index of the point to return.

Returns: The i-th point of the triangle.

◆ quality() [1/2]

template<PointConcept PointT>

ScalarType vcl::Triangle< PointT >::quality ( ) const

inline

Calculates the quality measure of the triangle.

The quality measure is computed as 2 times the triangle's area divided by the square of the length of its longest edge. The resulting value is in the range [0.0, 0.866], where 0.0 represents a degenerate triangle and 0.866 represents an equilateral triangle.

Returns: The quality measure of the triangle.

Note: If the area of the triangle is zero (i.e., the vertices are collinear), the function returns 0.0.

◆ quality() [2/2]

template<PointConcept PointT>

static ScalarType vcl::Triangle< PointT >::quality	(	const PointT &	p0,
		const PointT &	p1,
		const PointT &	p2
	)

inlinestatic

Calculates the quality measure of a triangle, given its three vertices.

The quality measure is computed as 2 times the triangle's area divided by the square of the length of its longest edge. The resulting value is in the range [0.0, 0.866], where 0.0 represents a degenerate triangle and 0.866 represents an equilateral triangle.

Parameters

[in]	p0	The first vertex of the triangle.
[in]	p1	The second vertex of the triangle.
[in]	p2	The third vertex of the triangle.

Returns: The quality measure of the triangle.

Note: If the area of the triangle is zero (i.e., the vertices are collinear), the function returns 0.0.

◆ qualityMeanRatio() [1/2]

template<PointConcept PointT>

ScalarType vcl::Triangle< PointT >::qualityMeanRatio ( ) const

inline

Compute the mean ratio of the triangle shape quality measure.

The function computes the mean ratio shape quality measure of the triangle. The mean ratio is defined as 2 * sqrt(a * b) / (a + b), where a and b are the eigenvalues of the M^tM transformation matrix into a regular simplex. The mean ratio is a scalar value in the range [0, 1] that describes the triangle quality, where 0 means the triangle is degenerate, and 1 means it is perfectly equilateral.

Returns: The mean ratio shape quality measure of the triangle.

Note: If the three points are collinear or form a degenerate triangle, the function returns 0.

◆ qualityMeanRatio() [2/2]

template<PointConcept PointT>

static ScalarType vcl::Triangle< PointT >::qualityMeanRatio	(	const PointT &	p0,
		const PointT &	p1,
		const PointT &	p2
	)

inlinestatic

Compute the mean ratio of a triangle shape quality measure.

Given three points p0, p1, p2 representing a triangle, the function computes the mean ratio shape quality measure of the triangle. The mean ratio is defined as 2 * sqrt(a * b) / (a + b), where a and b are the eigenvalues of the M^tM transformation matrix into a regular simplex. The mean ratio is a scalar value in the range [0, 1] that describes the triangle quality, where 0 means the triangle is degenerate, and 1 means it is perfectly equilateral.

Parameters

[in]	p0	The first point of the triangle.
[in]	p1	The second point of the triangle.
[in]	p2	The third point of the triangle.

Returns: The mean ratio shape quality measure of the triangle.

Note: The function assumes that the three points are not collinear and form a valid triangle. If the three points are collinear or form a degenerate triangle, the function returns 0.

◆ qualityRadii() [1/2]

template<PointConcept PointT>

ScalarType vcl::Triangle< PointT >::qualityRadii ( ) const

inline

Compute a shape quality measure of the triangle.

This function computes the quality measure of a triangle based on the ratio between its inradius and circumradius.

Returns: A value between 0 and 1 that represents the quality of the triangle shape. A value of 1 means the triangle is perfectly equilateral, while lower values indicate more distorted shapes (i.e., halfsquare: 0.81). A value of 0 is returned when the triangle is degenerate (i.e., it has zero area).

◆ qualityRadii() [2/2]

template<PointConcept PointT>

static ScalarType vcl::Triangle< PointT >::qualityRadii	(	const PointT &	p0,
		const PointT &	p1,
		const PointT &	p2
	)

inlinestatic

Compute a shape quality measure of the triangle composed by points p0, p1, p2.

This function computes the quality measure of a triangle based on the ratio between its inradius and circumradius. The function takes three points (p0, p1, p2) representing the vertices of the triangle.

Parameters

[in]	p0	The first vertex of the triangle.
[in]	p1	The second vertex of the triangle.
[in]	p2	The third vertex of the triangle.

Returns: A value between 0 and 1 that represents the quality of the triangle shape. A value of 1 means the triangle is perfectly equilateral, while lower values indicate more distorted shapes (i.e., halfsquare: 0.81). A value of 0 is returned when the triangle is degenerate (i.e., it has zero area).

◆ sideLength() [1/2]

template<PointConcept PointT>

ScalarType vcl::Triangle< PointT >::sideLength	(	const PointT &	p0,
		const PointT &	p1,
		const PointT &	p2,
		uint	i
	)		const

inline

Returns the length of the i-th side of the triangle composed by the points p0, p1, and p2.

Parameters

[in]	p0	first point of the triangle.
[in]	p1	second point of the triangle.
[in]	p2	third point of the triangle.
[in]	i	Index of the side.

Returns: The length of the i-th side of the triangle.

◆ sideLength() [2/2]

template<PointConcept PointT>

ScalarType vcl::Triangle< PointT >::sideLength ( uint i ) const

inline

Returns the length of the i-th side of the triangle.

Parameters

[in] i Index of the side.

Returns: The length of the i-th side of the triangle.

◆ sideLength0()

template<PointConcept PointT>

ScalarType vcl::Triangle< PointT >::sideLength0 ( ) const

inline

Returns the length of the first side of the triangle.

Returns: The length of the first side of the triangle.

◆ sideLength1()

template<PointConcept PointT>

ScalarType vcl::Triangle< PointT >::sideLength1 ( ) const

inline

Returns the length of the second side of the triangle.

Returns: The length of the second side of the triangle.

◆ sideLength2()

template<PointConcept PointT>

ScalarType vcl::Triangle< PointT >::sideLength2 ( ) const

inline

Returns the length of the third side of the triangle.

Returns: The length of the third side of the triangle.

◆ size()

template<PointConcept PointT>

constexpr uint vcl::Triangle< PointT >::size ( ) const

inlineconstexpr

Returns the number of points of the triangle.

Returns: 3

◆ weightedBarycenter() [1/3]

template<PointConcept PointT>

PointT vcl::Triangle< PointT >::weightedBarycenter ( const Point3< ScalarType > & w ) const

inline

Computes the weighted barycenter of the triangle.

Given three weights corresponding to the three triangle points, this function computes the weighted barycenter of the triangle.

Parameters

[in] w The weights of the three points of the triangle.

Returns: The weighted barycenter of the triangle.

◆ weightedBarycenter() [2/3]

template<PointConcept PointT>

static PointT vcl::Triangle< PointT >::weightedBarycenter	(	const PointT &	p0,
		const PointT &	p1,
		const PointT &	p2,
		ScalarType	w0,
		ScalarType	w1,
		ScalarType	w2
	)

inlinestatic

Computes the weighted barycenter of a triangle composed of three points.

Given three points and their corresponding weights, this function computes the weighted barycenter of the triangle they form.

Parameters

[in]	p0	The first point of the triangle.
[in]	w0	The weight of the first point of the triangle.
[in]	p1	The second point of the triangle.
[in]	w1	The weight of the second point of the triangle.
[in]	p2	The third point of the triangle.
[in]	w2	The weight of the third point of the triangle.

Returns: The weighted barycenter of the triangle formed by p0, p1 and p2.

◆ weightedBarycenter() [3/3]

template<PointConcept PointT>

PointT vcl::Triangle< PointT >::weightedBarycenter	(	ScalarType	w0,
		ScalarType	w1,
		ScalarType	w2
	)		const

inline

Computes the weighted barycenter of the triangle.

Given three weights corresponding to the three triangle points, this function computes the weighted barycenter of the triangle.

Parameters

[in]	w0	The weight of the first point of the triangle.
[in]	w1	The weight of the second point of the triangle.
[in]	w2	The weight of the third point of the triangle.

Returns: The weighted barycenter of the triangle.

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

vclib/core/include/vclib/space/core/triangle.h

Public Types

Public Member Functions

Static Public Member Functions

Static Public Attributes

Private Attributes

Member Function Documentation

◆ area() [1/2]

◆ area() [2/2]

◆ barycenter() [1/2]

◆ barycenter() [2/2]

◆ barycentricCoordinatePoint() [1/2]

◆ barycentricCoordinatePoint() [2/2]

◆ circumcenter() [1/2]

◆ circumcenter() [2/2]

◆ normal() [1/2]

◆ normal() [2/2]

◆ perimeter() [1/2]

◆ perimeter() [2/2]

◆ point()

◆ quality() [1/2]

◆ quality() [2/2]

◆ qualityMeanRatio() [1/2]

◆ qualityMeanRatio() [2/2]

◆ qualityRadii() [1/2]

◆ qualityRadii() [2/2]

◆ sideLength() [1/2]

◆ sideLength() [2/2]

◆ sideLength0()

◆ sideLength1()

◆ sideLength2()

◆ size()

◆ weightedBarycenter() [1/3]

◆ weightedBarycenter() [2/3]

◆ weightedBarycenter() [3/3]