Class representing a polygon with 3 points and its member functions. More...

#include <Triangle.hpp>

Collaboration diagram for Triangle:

Classes
struct	circumcircle
	Circumcircle object. More...

Public Member Functions
	Triangle ()
	Default constructor.

	Triangle (int index, IMesh *owner)
	Constructor populating index and owner. More...

	~Triangle ()
	Default destructor.

void	calcCircumcircle ()
	Calculate the circumcircle of the Triangle. More...

bool	circumcircleContainsPoint (const Eigen::Vector2d &p) const
	Check if the circumcircle of the Triangle contains a point. More...

Eigen::Vector3d	barycentric (const Eigen::Vector2d &p) const
	Get the barycentric coordinates of a point in relation to the triangle. More...

bool	containsPoint (const Eigen::Vector2d &p) const
	Check if the Triangle contains a point. More...

double	area () const
	Calculate the area of the triangle in 2d (x & y coords) More...

int	getIndex () const
	Accessor for private member index. More...

void	setIndex (int i)
	Mutator for private member index. More...

const std::vector< int > &	getVertices () const
	Accessor for private member vertices. More...

void	setVertices (const std::vector< int > &vertices)
	Mutator for private member vertices. More...

const std::vector< double > &	getAttributes () const
	Accessor for private member attributes. More...

void	setAttributes (const std::vector< double > &attributes)
	Mutator for private member attributes. More...

const circumcircle &	getCc () const
	Accessor for private member cc. More...

void	setCc (const circumcircle &cc)
	Mutator for private member cc. More...

const std::vector< IMesh::edge > &	getEdges () const
	Accessor for private member edges. More...

void	setEdges (const std::vector< IMesh::edge > &edges)
	Mutator for private member edges. More...

IMesh *	getOwner () const
	Accessor for private member owner. More...

bool	operator== (const Triangle &rhs) const
	Equality operator. More...

bool	operator!= (const Triangle &rhs) const
	Non-equality operator. More...

Private Attributes
int	index
	Index of the triangle (loaded from file)

circumcircle	cc
	Circumcircle of the current triangle.

IMesh *	owner
	Pointer to interface class of the Mesh the Triangle is part of.

std::vector< double >	attributes
	Vector of attributes of the Triangle (16 points of precision)

std::vector< IMesh::vertInd >	vertices
	Vector of vertex indices making up the Triangle.

std::vector< IMesh::edge >	edges
	Vector of edges making up the Triangle.

Friends
std::istream &	operator>> (std::istream &is, Triangle &triangle)
	Input stream operator. More...

std::ostream &	operator<< (std::ostream &os, Triangle &triangle)
	Output stream operator. More...

std::ofstream &	operator<< (std::ofstream &ofs, Triangle &triangle)
	Output filestream operator. More...

Detailed Description

Class representing a polygon with 3 points and its member functions.

Class Documentation

◆ Triangle::circumcircle

struct Triangle::circumcircle

Circumcircle object.

Collaboration diagram for Triangle::circumcircle:

Class Members
double	radius	radius of the circumcircle
double	x	x coordinate of the circumcentre
double	y	y coordinate of the circumcentre

Constructor & Destructor Documentation

◆ Triangle()

Triangle::Triangle	(	int	index,
		IMesh *	owner
	)

inline

Constructor populating index and owner.

Parameters

index	Index of Triangle according to file
owner	Pointer to Mesh the Triangle is a part of

Member Function Documentation

◆ area()

double Triangle::area ( ) const

Calculate the area of the triangle in 2d (x & y coords)

Returns: area of triangle

Area of triangle can be computed given a triangle with points represented by vector \( \mathbf{A, B, C}\)

\[ A_T = \frac{|\mathbf{A}-\mathbf{B}| |\mathbf{B}-\mathbf{C}|}{2} \]

◆ barycentric()

Eigen::Vector3d Triangle::barycentric ( const Eigen::Vector2d & p ) const

Get the barycentric coordinates of a point in relation to the triangle.

Parameters

p	2 element double-precision Eigen3 vector storing the point in cartesian coordinates

Returns: 3 element double-precision Eigen3 vector storing the poit in barycentric coordinates

Given a point \(r = \left(\begin{matrix}x \\ y\end{matrix}\right)\) and a Triangle made up of points \(r_1, r_2, r_3\) where \(r_i = \left(\begin{matrix}x_i\\ y_i\end{matrix}\right)\), the barycentric coordinates of p, \((\lambda_1, \lambda_2, \lambda_3)\) can be determined

\[ \left(\begin{matrix}\lambda_1 \\ \lambda_2\end{matrix}\right) = \left(\begin{matrix} x_1-x_3 & x_2-x_3 \\ y_1-y_3 & y_2-y_3 \\ \end{matrix}\right)^{-1} \left( \left(\begin{matrix}x \\ y\end{matrix}\right)-\left(\begin{matrix}x_3\\ y_3\end{matrix}\right) \right) \]

\[ \lambda_3 = 1 - \lambda_1 - \lambda_2 \]

◆ calcCircumcircle()

void Triangle::calcCircumcircle ( )

Calculate the circumcircle of the Triangle.

Given a Triangle made up of points \(r_1, r_2, r_3\) where \(r_i = \left(\begin{matrix}x_i\\ y_i\end{matrix}\right)\), the circumcentre of the triangle \((O_x, O_y)\) and the circumcircle's radius \(R\) can be found from

\[ \mathbf{O} = \left(\begin{matrix} 2O_x \\ 2O_y \\ R^2 - O_x^2 - O_y^2 \end{matrix}\right) \]

\[ \left(\begin{matrix} x_0^2 + y_0^2 \\ x_1^2 + y_1^2 \\ x_2^2 + y_2^2 \end{matrix}\right) = \mathbf{O}\left(\begin{matrix} x_0 & y_0 & 1 \\ x_1 & y_1 & 1 \\ x_2 & y_2 & 1 \end{matrix}\right) \]

So by solving for \(\mathbf{O}\) the circumcircle's data can be found

◆ circumcircleContainsPoint()

bool Triangle::circumcircleContainsPoint ( const Eigen::Vector2d & p ) const

Check if the circumcircle of the Triangle contains a point.

Parameters

p	2 element double-precision Eigen3 vector storing the point

Returns: Whether the circumcircle contains the point

Given a point \(\mathbf{p}\) and the centre of a circumcirclecircle \(\mathbf{c}\), its distance from the circumcentre can be found

\[ d = |\mathbf{p}-\mathbf{c}| \]

If \(d < \) circumcircle::radius then the point is inside the circumcircle

◆ containsPoint()

bool Triangle::containsPoint ( const Eigen::Vector2d & p ) const

Check if the Triangle contains a point.

Parameters

p	2 element double-precision Eigen3 vector storing the point

Returns: Whether the triangle contains the point

First checks if point is inside pre-computed circumcircle, if it is, computes barycentric coordinates of the point If all barycentric coordinates \( \lambda_i >= 0\) then point is inside triangle

◆ getAttributes()

const std::vector< double > & Triangle::getAttributes ( ) const

Accessor for private member attributes.

Returns: vector of triangle attributes

◆ getCc()

const Triangle::circumcircle & Triangle::getCc ( ) const

Accessor for private member cc.

Returns: struct describing the circumcircle of the triangle

◆ getEdges()

const std::vector< std::pair< int, int > > & Triangle::getEdges ( ) const

Accessor for private member edges.

Returns: vector of edges making up the triangle

◆ getIndex()

int Triangle::getIndex ( ) const

Accessor for private member index.

Returns: index of Triangle or -1 if not part of mesh

◆ getOwner()

IMesh * Triangle::getOwner ( ) const

Accessor for private member owner.

Returns: pointer to owning Mesh interface class

◆ getVertices()

const std::vector< int > & Triangle::getVertices ( ) const

Accessor for private member vertices.

Returns: vector of vertex indices

◆ operator!=()

bool Triangle::operator!= ( const Triangle & rhs ) const

Non-equality operator.

Parameters

rhs

Returns

◆ operator==()

bool Triangle::operator== ( const Triangle & rhs ) const

Equality operator.

Parameters

rhs

Returns

◆ setAttributes()

void Triangle::setAttributes ( const std::vector< double > & attributes )

Mutator for private member attributes.

Parameters

attributes vector of triangle attributes

◆ setCc()

void Triangle::setCc ( const circumcircle & cc )

Mutator for private member cc.

Parameters

cc	struct describing the circumcircle of the triangle

◆ setEdges()

void Triangle::setEdges ( const std::vector< IMesh::edge > & edges )

Mutator for private member edges.

Parameters

edges vector of edges making up the triangle

◆ setIndex()

void Triangle::setIndex ( int i )

Mutator for private member index.

Parameters

i	index of Triangle

◆ setVertices()

void Triangle::setVertices ( const std::vector< int > & vertices )

Mutator for private member vertices.

Parameters

vertices vector of vertex indices

Friends And Related Function Documentation

◆ operator<< [1/2]

std::ofstream & operator<<	(	std::ofstream &	ofs,
		Triangle &	triangle
	)

friend

Output filestream operator.

Parameters

ofs
triangle

Returns

◆ operator<< [2/2]

std::ostream & operator<<	(	std::ostream &	os,
		Triangle &	triangle
	)

friend

Output stream operator.

Parameters

os
triangle

Returns

◆ operator>>

std::istream & operator>>	(	std::istream &	is,
		Triangle &	triangle
	)

friend

Input stream operator.

Parameters

is
triangle

Returns

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

src/Triangle.hpp
src/Triangle.cpp

Classes

Public Member Functions

Private Attributes

Friends

Detailed Description

Class Documentation

◆ Triangle::circumcircle

Constructor & Destructor Documentation

◆ Triangle()

Member Function Documentation

◆ area()

◆ barycentric()

◆ calcCircumcircle()

◆ circumcircleContainsPoint()

◆ containsPoint()

◆ getAttributes()

◆ getCc()

◆ getEdges()

◆ getIndex()

◆ getOwner()

◆ getVertices()

◆ operator!=()

◆ operator==()

◆ setAttributes()

◆ setCc()

◆ setEdges()

◆ setIndex()

◆ setVertices()

Friends And Related Function Documentation

◆ operator<< [1/2]

◆ operator<< [2/2]

◆ operator>>