Triangle Class Reference

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.
	~Triangle ()
	Default destructor.
void	calcCircumcircle ()
	Calculate the circumcircle of the Triangle.
bool	circumcircleContainsPoint (const Eigen::Vector2d &p) const
	Check if the circumcircle of the Triangle contains a point.
Eigen::Vector3d	barycentric (const Eigen::Vector2d &p) const
	Get the barycentric coordinates of a point in relation to the triangle.
bool	containsPoint (const Eigen::Vector2d &p) const
	Check if the Triangle contains a point.
double	area () const
	Calculate the area of the triangle in 2d (x & y coords)
int	getIndex () const
	Accessor for private member index.
void	setIndex (int i)
	Mutator for private member index.
const std::vector< int > &	getVertices () const
	Accessor for private member vertices.
void	setVertices (const std::vector< int > &vertices)
	Mutator for private member vertices.
const std::vector< double > &	getAttributes () const
	Accessor for private member attributes.
void	setAttributes (const std::vector< double > &attributes)
	Mutator for private member attributes.
const circumcircle &	getCc () const
	Accessor for private member cc.
void	setCc (const circumcircle &cc)
	Mutator for private member cc.
const std::vector< IMesh::edge > &	getEdges () const
	Accessor for private member edges.
void	setEdges (const std::vector< IMesh::edge > &edges)
	Mutator for private member edges.
IMesh *	getOwner () const
	Accessor for private member owner.
bool	operator== (const Triangle &rhs) const
	Equality operator.
bool	operator!= (const Triangle &rhs) const
	Non-equality operator.

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.
std::ostream &	operator<< (std::ostream &os, Triangle &triangle)
	Output stream operator.
std::ofstream &	operator<< (std::ofstream &ofs, Triangle &triangle)
	Output filestream operator.

Detailed Description

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

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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 Symbol 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

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

• src/Triangle.hpp
• src/Triangle.cpp