The TriangleWrapper class is a wrapper around a N-Dimensional triangle. More...

#include <vclib/space/core/triangle_wrapper.h>

Public Types
using	ScalarType = PointT::ScalarType

using	PointType = PointT

Public Member Functions
	TriangleWrapper (const PointT &p0, const PointT &p1, const PointT &p2)
	Constructs a triangle wrapper around the three input points.

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

const PointT &	point (uint i) const

const PointT &	point0 () const

const PointT &	point1 () const

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

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.

Static Public Attributes
static const uint	DIM = PointT::DIM
	Dimension of the triangle.

Private Attributes
const PointT &	mPoint0

const PointT &	mPoint1

const PointT &	mPoint2

Detailed Description

template<PointConcept PointT>
class vcl::TriangleWrapper< PointT >

The TriangleWrapper class is a wrapper around a N-Dimensional triangle.

The dimension of the triangle is determined by the dimension of the points it is composed of.

The class does not store the triangle points, but it provides a wrapper around them. This class is useful when the triangle points are already stored somewhere else and the user does not want to copy them, but have access to the a triangle interface.

This means that the TriangleWrapper object must live as long as the points it wraps. If the points are destroyed, the TriangleWrapper object becomes invalid.

This class cannot be copied or moved, and has just one constructor that takes three points as input. The points are passed by const reference, and their references are stored inside the class.

Constructor & Destructor Documentation

◆ TriangleWrapper()

template<PointConcept PointT>

vcl::TriangleWrapper< PointT >::TriangleWrapper	(	const PointT &	p0,
		const PointT &	p1,
		const PointT &	p2
	)

inline

Constructs a triangle wrapper around the three input points.

The input points are not copied, and this class just stores their references.

Parameters

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

Member Function Documentation

◆ area()

template<PointConcept PointT>

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

inline

Computes the area of the triangle.

Returns: The area of the triangle.

◆ barycenter()

template<PointConcept PointT>

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

inline

Computes the barycenter of the triangle.

Returns: The barycenter of the triangle.

◆ barycentricCoordinatePoint() [1/2]

template<PointConcept PointT>

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

inline

◆ barycentricCoordinatePoint() [2/2]

template<PointConcept PointT>

PointT vcl::TriangleWrapper< PointT >::barycentricCoordinatePoint	(	ScalarType	b0,
		ScalarType	b1,
		ScalarType	b2
	)		const

inline

◆ circumcenter()

template<PointConcept PointT>

PointT vcl::TriangleWrapper< 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.

◆ normal()

template<PointConcept PointT>

PointT vcl::TriangleWrapper< 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.

◆ perimeter()

template<PointConcept PointT>

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

inline

Computes the perimeter of the triangle.

Returns: The perimeter of the triangle.

◆ point()

template<PointConcept PointT>

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

inline

◆ point0()

template<PointConcept PointT>

const PointT & vcl::TriangleWrapper< PointT >::point0 ( ) const

inline

◆ point1()

template<PointConcept PointT>

const PointT & vcl::TriangleWrapper< PointT >::point1 ( ) const

inline

◆ point2()

template<PointConcept PointT>

const PointT & vcl::TriangleWrapper< PointT >::point2 ( ) const

inline

◆ quality()

template<PointConcept PointT>

ScalarType vcl::TriangleWrapper< 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.

◆ qualityMeanRatio()

template<PointConcept PointT>

ScalarType vcl::TriangleWrapper< 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.

◆ qualityRadii()

template<PointConcept PointT>

ScalarType vcl::TriangleWrapper< 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).

◆ sideLength()

template<PointConcept PointT>

ScalarType vcl::TriangleWrapper< 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::TriangleWrapper< 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::TriangleWrapper< 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::TriangleWrapper< 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::TriangleWrapper< PointT >::size ( ) const

inlineconstexpr

Returns the number of points of the triangle.

Returns: 3

◆ weightedBarycenter() [1/2]

template<PointConcept PointT>

PointT vcl::TriangleWrapper< 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]	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.

◆ weightedBarycenter() [2/2]

template<PointConcept PointT>

PointT vcl::TriangleWrapper< 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_wrapper.h

Public Types

Public Member Functions

Static Public Attributes

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ TriangleWrapper()

Member Function Documentation

◆ area()

◆ barycenter()

◆ barycentricCoordinatePoint() [1/2]

◆ barycentricCoordinatePoint() [2/2]

◆ circumcenter()

◆ normal()

◆ perimeter()

◆ point()

◆ point0()

◆ point1()

◆ point2()

◆ quality()

◆ qualityMeanRatio()

◆ qualityRadii()

◆ sideLength()

◆ sideLength0()

◆ sideLength1()

◆ sideLength2()

◆ size()

◆ weightedBarycenter() [1/2]

◆ weightedBarycenter() [2/2]